I numeri di Friedman noti
La tabella seguente riporta i numeri di Friedman noti nelle basi fino a 20 e tutti i numeri di Friedman fino a 105 in base 10; tutti i numeri sono scritti nella base indicata nella colonna di sinistra, omessa poi nei numeri per semplicità (Phillipe Fondanaiche, Eric Friedman, Trevor Green, Mike Reid, e Joe DeVincentis).
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Base |
Numeri di Friedman |
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2 |
11001 = 10110, 11011 = 110 + 11, 111111 = (11 + 1)11 – 1, 1001111 = 11100 – 1 – 1, 1010001 = 11100 + 0 + 0, 1010011 = 11100 + 10, 1100011 = 101010 – 1, 1100100 = 101010 + 0, 1100101 = 101010 + 1, 1111001 = 1 • 101110, 1111010 = 101110 + 1, 1111011 = 10111 – 1 – 1, 1111100 = 10111 – 1 – 0, 1111101 = (11 + 1 + 1)10 + 1, 1111110 = (1 + 1)111 – 10, 1111111 = (1 + 1)111 – 1 • 1, 10001110 = 110010 – 10, 10001111 = 110010 – 1 • 1, 10011111 = 11 • 110101, 10100111 = 110110 – 10, 10101001 = 110110 + 0 + 0, 10101011 = 110110 + 10, 10101111 = 111 • 11001, 10111101 = 11 • (10011 – 1),10111111 = 11 • (1 + 1)110 – 1, 11010110 = 11010 + 1 – 10, 11010111 = 11010 + 1 – 1 • 1, 11011000 = 11011 + 0 + 0 + 0, 11011001 = 11011 + 0 + 0 + 1, 11011010 = 11011 + 0 + 10, 11011011 = 11011 + 0 + 11, 11011100 = 11011 + 100, 11011101 = 11011 + 101, 11011110 = 11011 + 110, 11011111 = 11011 + 111, 11100001 = (10000 – 1)11, 11101101 = 11101 – 110, 11101110 = 11101 – 101, 11101111 = 11101 – 11 – 1, 11110001 = 11101 – 10 – 0, 11110010 = –1 + 11100 + 1 + 0, 11110011 = 1 + 11100 + 1 – 1, 11110100 = 1 + 11101 + 0 + 0, 11110101 = 1 + 11101 + 0 + 1, 11110110 = 1 + 11101 + 10, 11110111 = 1 + 11101 + 11, 11111001 = 10111 • 10 – 1, 11111010 = 10111 • (1 + 1) + 0, 11111011 = 10111 • (1 + 1) + 1, 11111100 = (10111 + 1) • 10, 11111101 = 10(1+1)11 – 11, 11111110 = (11 + 1)11 + 1 – 10, 11111111 = (11 + 1)11 + 1 – 1 • 1, 100011110 = 1000110 – 11, 100011111 = 100011 + 1 – 1 – 1, 100100001 = 1000110 + 0 + 0, 100100011 = 1000110 + 10, 100101111 = 1100101 • 11, |
|
3 |
121 = 112, 221 = 122, 1022 = 202 – 1, 1122 = 2 • 211, 1211 = 211 + 1, 1212 = 1 + 212, 2022 = 220 – 2, 2101 = (1 + 1)20, 2102 = 220 + 1, 10122 = 1012 – 2, 10201 = 1012 + 0, 11022 = 2 • 2011, 11122 = 1 • 121 + 2, 11202 = (1 + 1)20 • 2, 11220 = 2 • 2110, 12021 = 1102 – 2, 12022 = –1 + (20 • 2)2, 12100 = 1102 + 0, 12101 = 1102 + 1, 12102 = 1102 + 2, 12122 = 2 • 2211, 12221 = 12 • 212, 21021 = 1122 + 0, 21102 = 2 • 1012, 22021 = 1202 – 2, 22100 = 1202 + 0, 22101 = 1202 + 1, 22102 = 1202 + 2, 100111 = (10 + 0 + 1)11, 100112 = 2100 – 1 + 1, 101122 = 2 • 1102 – 1, 101201 = (200 – 1)1 + 1, 101202 = (200 – 1)2 + 1, 101222 = 11 • 2202, 102202 = 2002 – 21, 102212 = 1 • 12 • 220, 102220 = 2002 – 2 – 1, 102221 = (201 – 1)2 – 2, |
|
4 |
121 = 112, 123 = (1 + 2)3, 1203 = 3 • 201, 1230 = 3 • 210, 1321 = 231 + 1, 1322 = 232 + 1, 1331 = (3 + 1 + 1)3, 1332 = (3 + 2)3 + 1, 2032 = 302 – 2, 2213 = 312 – 2, 3120 = 123 + 0, 3121 = 123 + 1, 3122 = 123 + 2, 3123 = 3 + 123, 3322 = 2 • (3 • 2)3, 10132 = 1012 – 3, 10201 = 1012 + 0, 10221 = 21 • 201, 11113 = 131 + 1 + 1, 11133 = 3 • 1311, 11221 = (111 – 2)2, 11313 = 113 • 1 • 3, 12003 = 3 • 2001, 12030 = 3 • 2010, 12031 = 1102 – 3, 12100 = 1102 + 0, 12101 = 1102 + 1, 12102 = 1102 + 2, 12103 = 1102 + 3, 12232 = 2 • 123 – 2, 12233 = –1 + 2 • (2 • 3)3, 12300 = 3 • 2100, 12303 = 3 • (302 + 1), 12321 = ((1 + 2) • 13)2, 12323 = (3 • 13)2 + 2, 13023 = 21 • 303, 13211 = 2 • 311 + 1, 13212 = 2 • 312 – 1, 13222 = 132 • 22, 13233 = 313 • 32, 13322 = 23 • 3 – 12, |
|
5 |
121 = 112, 224 = 22 + 4, 1232 = 22 • 31, 1241 = 241 + 1, 1242 = 1 + 242, 1331 = (3 • (1 + 1))3, 1332 = (3 • 2)3 + 1, |
|
6 |
24 = 24, 52 = 25, 121 = 112, 124 = 4 • 21, 133 = 3 • 31, 143 = –1 + 43, 144 = 44 – 1, 213 = 132, 1043 = 34 + 1 + 0, 1053 = 35 + 10, 1135 = 5 • 131, 1204 = 4 • 201, 1224 = 2 • 412, 1240 = 4 • 210, 1242 = 2 • 421, 1252 = 5 • 122, 1303 = 3 • 301, 1330 = 3 • 310, 1352 = 312 – 5, 1353 = 3 • 315, 1423 = 23 • 41, 1425 = 21 • 45, 1524 = 4 • 251, 1533 = 3 • 351, 2212 = 2(2 + 1)2, 232 + 1, 2235 = 352 – 2, 2241 = (41 – 2)2, 2355 = 35 • 52, 2400 = 402 + 0, 2401 = 402 + 1, 2402 = 2 + 402, 2403 = 402 + 3, 2404 = 402 + 4, 2405 = 402 + 5, 2514 = 54 – 2 – 1, 2515 = –2 + 5–1 + 5, 2521 = 1 • 52 + 2, 2534 = 54 + 32, 2535 = (2 + 53) • 5, |
|
7 |
121 = 112, 143 = 34 – 1, 144 = (–1 + 4)4, 264 = 4 • 62, 514 = (5 – 1)4, 1155 = 15 • 51, 1253 = 312 – 5, 1263 = 2 • 36 – 1, 1331 = (1 + 1)3 • 3, 1332 = 23 • 3 + 1, 1452 = 51 • 42, 1541 = 54 – 11, 1544 = –1 + 54 – 4, 1545 = 1 + 54 – 5, 1551 = –1 + 55 – 1, 1552 = 1 • (5 • 5)2, 1553 = 1 + 5 • 53, |
|
8 |
33 = 33, 121 = 112, 125 = 5 • 21, 143 = 3 • 41, 251 = 152, 257 = 7 • 52, 326 = 63 – 2, |
|
9 |
121 = 112, 134 = 4 • 31, 314 = (3 + 1)4, 628 = 8 • 26, 1304 = 4 • 301, 1326 = 2 • 613, 1340 = 31 • 40, 1354 = 45 – 1 • 3, 1357 = 1 • (7 – 3)5, 1362 = 2 • 631, 1363 = 3 • (1 + 6)3, 1438 = 18 • 43, 1456 = 4 • 6 • 51, 2086 = 20 + 8 • 6, 2132 = (32 – 1)2, 2136 = 6 • 321, 2467 = 472 – 6, 2472 = –2 + 472, 2474 = 474 – 2, |
|
10 |
25 = 52, 121 = 112, 125 = 51 + 2, 126 = 6 • 21, 127 = –1 + 27, 128 = 28 – 1, 153 = 3 • 51, 216 = 62 + 1, 289 = (8 + 9)2, 343 = (3 + 4)3, 347 = 73 + 4, 625 = 56 – 2, 688 = 8 • 86, 736 = 7 + 36, 1022 = 210 – 2, 1024 = (4 – 2)10, 1206 = 6 • 201, 1255 = 5 • 251, 1260 = 6 • 210, 1285 = (1 + 28) • 5, |
|
11 |
121 = 112, 2A9 = (A + 9)2, 603 = 36 + 0, 1163 = 361 + 1, 1533 = 53 • 31, 15A2 = 2A + 15,16A3 = A • (63 + 1), 1974 = 74 + 91, 1A18 = A • (1 + 1)8, 2343 = 3 • 42 + 3, 2345 = 2 + 3 • 45, 2494 = (44 + 9)2, 2783 = 82 • 37, 2794 = 29 + 4 • 7, 2883 = (8 • 8 – 3)2, 3094 = (–30 + 9)4, 3317 = (3 – 1) • 37, 3518 = 18 • 35, 362A = 632 – A, 3642 = 632 + 4, 3879 = 7 • (93 – 8), 48A2 = 4 + (8 • A)2, 4A18 = (A – 1)4 – 8, 4A34 = 34 + 4 + A, 4A38 = 4 + A + 38, 4A98 = 94 + 10 • 8, 5287 = 725 • 8, 5327 = 27 • 35, 5478 = 7 • (45 + 8), 7739 = (7 + 7) • 93, 8A29 = 9A2 + 8, 90A2 = A02 – 9, 9A25 = A52 – 9, A428 = 4A • 28 |
|
12 |
121 = 112, 127 = 21 • 7, 135 = 31 • 5, 144 = 41 • 4, 163 = 61 • 3, 346 = 34 • 6, 368 = 86 – 3, 376 = 73 • 6, 441 = (4 + 1)4, 445 = 54 + 4, 114A = 141 • A, 1169 = 161 • 9, 1207 = 201 • 7, 1228 = 21 + 2 + 8, 1229 = 1 + 22 + 9, 122A = 2 • (2A + 1), 122B = 1 + 2 + 2B, 123B = 2B + 13, 1270 = 210 • 7, 12B9 = 2B + 91, 1305 = 301 • 5, 1323 = 32 • 3 + 1, 1350 = 310 • 5, 1404 = 401 • 4, 1428 = 814 • 2, 1440 = 410 • 4, 1476 = 74 – 6 – 1, 1477 = 74 – 7 + 1, 1481 = (8 – 1)4 • 1, 1482 = 841 • 2, 1544 = 1 • 54 • 4, 1603 = 601 • 3, 1630 = 610 • 3, 1826 = 81 • 26, 1924 = 91 • 24, 1A28 = A8 • 21, 1B53 = (–1 + B + 5)3, 2379 = 927 • 3, 2448 = (2 • 4)4 – 8, 2452 = 542 – 2, 2454 = –2 + 45 • 4, 2468 = 46 + 2 • 8, 2525 = 252 • 5, 2541 = (54 + 1)2, 2545 = 552 + 4, 257A = 5 • 7 • A2, 2636 = 6 • (36 – 2), 2779 = 79 • 72, 2815 = 582 + 1, 2942 = (–2 + 9)4 • 2, |
|
13 |
121 = 112, 237 = 27 • 3, 24A = A2 • 4, 1245 = (1 + 5)4 • 2, 1246 = 64 • 2 + 1, 1353 = 33 • 51, 1524 = (1 + 2) • 45, 1559 = 1 • 55 – 9, |
|
14 |
121 = 112, 128 = 21 • 8, 135 = 1 • 35, 144 = 1 • 44, 173 = 71 • 3, 237 = (3 • 7)2, 248 = 82 • 4, 288 = 82 • 8, 294 = 42 • 9, 396 = 36 – 9, 3A1 = (A – 1)3, |
|
15 |
26 = 62, 121 = 112, 136 = 31 • 6, 154 = 51 • 4, 336 = –3 + 36, 339 = 3–3 + 9, |
|
16 |
121 = 112, 129 = 21 • 9, 145 = 41 • 5, 183 = 81 • 3, 27D = 72 • D, 57C = 75 • C, 1209 = 201 • 9, 1236 = 612 • 3, 1263 = 621 • 3, 1290 = 21 • 90, 1405 = 401 • 5, 1450 = 41 • 50, |
|
17 |
121 = 112 |
|
18 |
121 = 112, 5B9 = B5 • 9, DGF = GD • F |
|
19 |
121 = 112 |
|
20 |
121 = 112 |
, 100111011 = 1101001 • 11, 100111110 = 1101010 • 11, 100111111 = 11101 • 1011, 101000011 = 1001010 – 1 – 0, 101000100 = 1001010 + 0 + 0, 101000101 = 1001010 + 0 + 1, 101000110 = 1001010 + 10, 101000111 = 1001010 + 11, 101001111 = 11111 – 1000, 101010101 = (1000 – 1)11 – 10, 101010110 = (1000 – 1)11 – 1 – 0, 101010111 = (101 + 0 + 10)11 • 1, 101011001 = (1000 – 1)11 + 10, 101011011 = 11111 + 100 + 0, 101011110 = 110010 • 111, 101011111 = 1110101 • 11, 101100111 = 1001110 – 1 – 1, 101101001 = 100111 + 1 + 0 + 0, 101101010 = 1001110 + 0 + 1, 101101011 = (1011 – 0)10 • 11, 
, 101110111 = (1 + 0 + 1 + 1) • 10111, 101111010 = (10011 – 1) • 110, 101111101 = (10111 – 1) • (10 + 1), 101111110 = 10111 • 11 – 10, 101111111 = 10111 • 11 – 1 • 1, 110001101 = 1010010 – 11, 110001110 = 1010010 – 1 – 1, 110001111 = 101001 + 1 – 1, 110010000 = 1010010 + 0 + 0, 110010001 = 1010010 + 0 + 1, 110010010 = 1010010 + 10, 110010011 = 1010010 + 11, 110010101 = 11100 • 101 + 0, 110101101 = (110010 – 1) • 11, 110101110 = (11010 + 1 – 1) • 10, 110101111 = 11010 + 1 • (1 + 1) – 1, 110110011 = (110010 + 1) • 11, 110110110 = 1010110 – 11, 110110111 = (11 • 111)10 – 10, 110111000 = 1010110 – 1 – 0, 110111001 = 1010110 • 1 • 1, 110111010 = 1010110 + 1 • 1, 110111011 = (11 • 111)10 + 10, 110111100 = 1010110 + 11, 110111111 = (1 + 1)110 • 111 – 1, 111001011 = 1111 • 10001, 111100010 = 1011010 – 10, 111100011 = 1011010 – 1 • 1, 111100100 = 101101 + 1 + 0 + 0, 111100101 = 111 + 100 • 10 – 1, 111100110 = (1 + 1 + 1)100 + 1 • 10, 111100111 = 111 + 100 • (1 + 1) + 1, 111101010 = 11110 • 1010, 111101100 = (11100 + 1) • 110, 
, 
, 
, 111111000 = (10111 + 1) • 100, 111111001 = –111 + (1 + 1)1001, 111111010 = 1011 • 11 – 110, 111111011 = 11 • (–1 + 1110)1 + 1, 111111100 = (111 + 1)11 – 100, 111111101 = (111 + 1)11 – 10 – 1, 111111110 = (111 + 1)11 – 1 – 1 – 0, 111111111 = (11 – 1)111 + 1 + 1 – 1, 1000001111 = (11000 – 1)10 – 10, 1000110111 = (1000 + 1)10 • 111, 1000111010 = 1100010 – 110, 1000111011 = 110001 + 1 – 101,1000111100 = 110001 + 1 – 100, 1000111101 = 110001 + 1 – 11 – 0, 1000111110 = (1000 • 11)1 + 1 – 10, 1000111111 = (1000 • 11)1 + 1 – 1 • 1, 1001001111 = 11 • 11000101, 1001010111 = 101010 • 110 – 1, 1001011011 = 11 • 11001001, 1001011101 = 101110 • 101 + 0, 1001011110 = (101010 + 1) • 110, 1001100101 = 101100 – 1100, 1001101011 = 101100 – 101 – 1, 1001101100 = –100 – 1 + 101100, 1001101101 = 101100 – 11 – 1, 1001101110 = 101100 – 11 – 1 • 0, 1001101111 = –1 + 0 + 0 – 1 + 10111 + 1, 1001110000 = 101100 – 1 – 0 – 0 – 0, 1001110001 = (100 + 1)11 + 0 + 0 + 0 + 1, 1001110010 = (100 + 1)1 • 100 + 1 + 0, 1001110011 = (100 + 1)1 • 100 + 1 + 1, 1001110100 = 101100 + 11 + 0 + 0, 1001110101 = 10111 + 1 + 100 + 0, 1001110110 = (10011 – 1) • 1010, 1001110111 = 10111 + 1 + 110 + 0, 1001111001 = 101100 + 1011, 1001111010 = 101100 + 1110, 1001111011 = (10111 – 1 – 0) • 101, 1001111100 = 101100 + 1011, 1001111101 = 11110 • 1101 + 0, 1001111110 = 10111 • 101 – 10, 1001111111 = (100 + 1) • (1 + 1)111 – 1, 
, 1010011110 = 1101010 – 110, 1010011111 = 110101 + 1 – 101, 1010100011 = 1101010 – 1 – 0 – 0, 1010100100 = 1101010 + 0 + 0 + 0, 1010100101 = 1101010 + 1 + 0 + 0, 1010100110 = 1101010 + 10 + 0, 1010100111 = 1101010 + 11 + 0, 1010101101 = (1000 – 1)11 • 10 – 1, 1010101110 = (101 + 0 + 10)11 • 10, 1010101111 = 10 • (10 + 101)11 + 1, 1010111011 = 11 • 11101001, 1010111100 = 101010 • 111, 1010111101 = 11110 – 11100, 1010111110 = 1111 • 11010, 1010111111 = (1 + 1)110 • 1011 – 1, 1011000111 = 11110 – 10010, 1011001001 = 11110 – 10000, 1011001011 = (110010 – 1) • 101, 1011001101 = 11110 – 1100, 1011001111 = 11001 + 1 • 101 – 1, 1011010001 = 11110 – 1000, 1011010010 = 10 • (–1 + 10100)10, 1011010011 = 11110 – 110 – 0 – 0, 1011010101 = 11110 – 10 – 10 – 0, 1011010110 = (1011 + 0)10 • 110, 1011010111 = (10 + 1)10 • (10 + 1) –1 – 1, 1011011000 = –1 + 0 + (1 + 10)110 + 0 + 0, 1011011001 = –1 + 0 + (1 + 10)110 + 0 + 1, 1011011010 = –1 + 0 + (1 + 10)110 + 10, 1011011011 = –1 + 0 + (1 + 10)110 + 11, 1011011100 = 10 + 1 + (10 + 1)110 + 0, 1011011101 = 10 + 1 + (10 + 1)110 + 1, 1011011110 = –1 + 110 + 11110, 1011011111 = ((10 + 1)101 + 1 + 1) • 11, 1011100001 = 11110 + 1000 + 0, 1011100011 = 11110 + 1010 + 0, 1011100101 = 11110 + 1100 + 0, 1011100111 = 11110 + 1110 + 0, 1011101001 = 11110 + 10010, 1011101010 = 11110 + 10001, 1011101101 = (10111 + 0) • 110 – 1, 1011101110 = (10111 + 0 • 1) • 110, 1011101111 = 10 • 11 • 10111 + 1, 1011110001 = 11110 + 11000, 1011110011 = 11110 + 11010, 1011110100 = 11010 • 10101, 1011110101 = 11110 + 11100, 1011110111 = 11110 + 11110, 1011111001 = 11110 + 10101, 1011111010 = (10111 – 1) • 110 + 0, 1011111011 = (10111 – 1) • 110 + 1, 1011111100 = ((1 + 1)1000 – 1) • 11 – 1, 1011111101 = (10(1 + 1)11 – 1) • (10 + 1), 1011111110 = (10111 • 11 – 1) • 10, 1011111111 = (1 + 0 + 1)(1 + 1)11 • 11 – 1, 1100001110 = 1110010 – 10 + 0, 1100001111 = 1110010 – 10 + 1, 1100011110 = (101001 + 1 – 1) • 10, 1100011111 = 101001 + 1 • (1 + 1) – 1, 1100101010 = 11100 • 1010 + 0, 1100101011 = 11100 • 1010 + 1, 
, 1100111111 = (1 + 1)110 • 1101 – 1, 1101000111 = 1110110 – 10 – 0, 1101001001 = 1110110 + 0 + 0 + 0, 1101001011 = 1110110 + 10 + 0, 1101001101 = 1110110 + 100, 1101001111 = 1110110 + 110, 1101011010 = (110010 – 1) • 110, 1101011011 = (11011 – 1) • 100 – 1, 1101011100 = (11010 + 1 – 1) • 100, 
, 
, 
, 1101100011 = 100011 + 1 • 11 + 0, 1101100110 = (110010 + 1) • 110, 1101101011 = (110 + 1) • (101 + 0)11, 1101110001 = 1010110 • 10 – 1, 1101110010 = 1010110 • 10 • 1, 1101110011 = 1010110 • (1 + 1) + 1, 1101110100 = (1010110 + 1) • 10, 1101111010 = 11100 • 1011 – 1, 1101111011 = (1 + 10)1 + 11 • 1011, 1101111100 = 1 + 1011 • 11100, 1101111101 = 1111010 – 111, 1101111110 = 10111 • 111 – 10, 1101111111 = (1 + 1 + 0)111 • 111 – 1, 1110000100 = (100000 – 10)1 + 1, 1110010110 = 1111 • 100010, 1110111011 = 1111110 – 110, 1110111101 = 111111 + 1 – 100, 1110111110 = 1111110 – 11 – 0, 1110111111 = ((1 + 1)101 – 1)1 + 1 – 1 – 1, 1111000000 = (100000 – 1)10 – 1, 1111000001 = (10101 – 1)10 + 0 + 0, 1111000010 = (100000 – 1)1 + 1 + 1, 1111000011 = (10101 – 1)10 + 10, 1111000110 = (1011010 – 1) • 10, 1111000111 = (101101 + 1 • 10) – 1, 1111001000 = 1011010 • 10 + 0, 1111001001 = 1011010 • 10 + 1, 1111001010 = (1011010 + 1) • 10, 1111001011 = –1 + 11 • 100101 + 1, 1111001100 = (1 + 1 + 1)100 + 1 • 100, 1111001101 = 11101 • 100 + 0 + 1, 1111001110 = 11101 • 100 + 10, 1111001111 = 11101 • 100 + 11, 1111010011 = 111010 • 101 – 1, 1111010100 = 11110 • 10100, 1111010101 = 1 + 111010 • 101, 1111011000 = (11100 + 1) • 1100, 1111011001 = (111010 + 1) • 101, 1111011010 = 101011 – 1110, 1111100000 = 101011 – 1000, 1111100010 = 101011 – 110 – 0, 1111100011 = 101011 – 101 • 1, 1111100100 = 101011 – 100 • 1, 1111100101 = –1111 + 100101, 1111100110 = (1011 – 1)11 – 10 – 0, 1111100111 = ((1 + 1)11 + 10 + 0)11 – 1, 1111101000 = 101011 + 1 • 1 • 0 • 0, 1111101001 = (1 + 1 + 1110)10 + 0 + 1, 1111101010 = 101011 + 1 + 1 + 1 • 0, 1111101011 = 1 + 1 + 1 • 1 + 101011, 1111101100 = 101011 + 101 – 1, 1111101101 = 101011 + 11 + 1 + 1, 1111101110 = 101011 + 111 – 1, 1111101111 = 111 + (–1 + 1011)11, 1111110000 = 110010 • 111 + 0, 1111110001 = 110010 • 111 + 1, 1111110010 = (1 + 1)1010 – 1110, 1111110011 = (1 + 1)1010 – 1101, 1111110100 = (1 + 1)1010 – 1100, 1111110101 = (11 + 1)101 – 1011, 1111110110 = (1 + 1) • 11 • 110110, 1111110111 = (11 + 1)101 – 111 + 1, 1111111000 = ((1 + 1)111 – 1) • 1000, 1111111001 = –111 + (1 + 1)1 + 1001, 1111111010 = –11 • (1 + 1) + (1 + 1)1010, 1111111011 = –11 – 1 + (11 + 1)101 – 1, 1111111100 = (1 + 1)(1 + 1)11 • 100, 1111111101 = ((1 + 1)11 • 11 – 1) • 10 – 1, 1111111110 = ((1 + 1 • 1)11 • 11 – 1) • 10, 1111111111 = ((1 + 1)111 + 11 – 1 • 1 • 1
, 110022 = 2 • 20011, 110122 = 2110 – 2 • 1, 110201 = 2110 – 1 • 0, 110202 = 2110 + 20, 110220 = 2 • 20110, 111022 = 2012 – 1 – 1, 111102 = 2011 + 1 + 1, 111220 = (1 + 2) • 1210, 112002 = 2 • 201001, 112012 = 10 • 221 – 1, 112020 = (1 + 1)20 • 20, 112021 = 10 • 221 + 1, 112022 = 10 • 221 + 2, 112112 = 1121 + 1 • 2, 112200 = 2 • 21100, 112202 = 2022 – 1 – 1, 112210 = 2021 + 1 – 1, 112211 = (211 – 2)1 + 1, 112212 = (211 – 2)2 + 1, 112220 = 2022 + 1 + 1, 120221 = 2 • (201 + 2 – 1), 121002 = 2 • (1020 + 1), 121012 = 2102 – 11, 121020 = 2102 – 10, 121021 = –1 + 2102 – 1, 121022 = 1 + 2102 – 2, 121100 = 2101 + 1 + 0, 121101 = 2101 + 1 + 1, 121102 = 2101 + 1 + 2, 121121 = 21 • 111 + 2, 
, 121202 = 2 • (1202 + 1), 121220 = 2 • 22110, 122012 = 22 • 2011, 122122 = 2112 – 22, 122201 = 2112 – 20, 122210 = 120 • 212, 122211 = 2112 – 2 – 1, 122212 = 2 • ((1 + 2)12 + 2), 122220 = (202 + 2)2 – 1, 122221 = (2 • (2 • 12 + 1))2, 200221 = 2102 – 20, 200222 = (2 + 0 + 0) • 222, 201121 = 2121 + 1 + 0, 201122 = 2122 + 1 + 0, 210022 = 2202 – 1 – 0, 211020 = 20 • 1012, 211212 = 1211 – 22, 211222 = 122 • 2 – 12, 212011 = (21 – 2)0 + 11, 212012 = 122 • 2 + 0 + 1, 212021 = 122 • 2 + 10, 212101 = 1211 + 20, 212112 = 12 • (221 – 1), 212122 = 12 • 221 – 2, 212201 = 12 • 221 + 0, 220221 = 2222 – 10, 220222 = (220 + 2)2 – 2, 221001 = (1001 – 2)2, 221021 = 2 • (2110 – 2), 221101 = 2 • 2110 – 1, 221102 = 2 • 211 + 0 + 2, 221110 = 2 • 2110 + 1, 221120 = 2 • (2110 + 2), 221221 = 21 • (2 + 12)2, 222200 = 202 • 202, 222201 = (1 + 2)20 – 22, 
, 222221 = (1 + 2)2 + 2 + 2 – 2
, 13331 = (1 + 1)3 • 3 – 3, 13332 = (–1 + 3)3 • 3 – 2, 21233 = (2 + 3)1 + 3 – 2, 21301 = 113 + 20, 21331 = 31 • 132, 21333 = 3 • (123 – 3), 22210 = 1222 + 0, 22211 = 1222 + 1, 22212 = 1222 + 2, 22213 = 1222 + 3, 22330 = 32 • 302, 22332 = 3 • 3222, 23031 = 312 – 30, 23102 = 2 • 1032, 23112 = 312 – 1 – 2, 23113 = –2 + 3(1 + 1) • 3, 23120 = 312 – 20, 23121 = (23 + 1)2 + 1, 23122 = 32 + 2 + 2 + 1, 23123 = 2 + 31 • 2 • 3, 23130 = 312 + 3 + 0, 23131 = 312 + 3 + 1, 23132 = 312 + 3 + 2, 23133 = 312 + 3 + 3, 23201 = 312 + 20, 23213 = 312 + 32, 23322 = 3 • (323 – 2), 31021 = 1312 + 0, 31323 = 31 + 3 • 23, 33211 = (21 + 1)3 – 3, 33212 = (32 + 1)3 – 2, 33220 = ((2 + 3) • 2)3 + 0, 33221 = ((2 + 3) • 2)3 + 1, 33222 = ((2 + 3) • 2)3 + 2, 33223 = 3 + ((3 + 2) • 2)3, 33232 = 223 + 3 + 3, 33312 = (3 + 3) • 312, 33322 = 2 • (23 • 3 – 3)
, 1443 = 44 – 13, 2123 = 322 – 1, 2124 = (24 + 1)2, 2244 = (4 • 4 + 2)2, 2333 = (–2 + 3 • 3)3, 2421 = (41 – 2)2, 2423 = 342 + 2, 2433 = 4 • 332, 3042 = 402 – 3, 3421 = 2 • 34 + 1, 3422 = 3 + 422, 4243 = 442 – 3, 4441 = (4 + 1)4 – 4, 10142 = 1012 – 4, 10201 = 1012 + 0, 10314 = 311 – 40, 10413 = 311 + 4 + 0, 11424 = 44 • 112, 12041 = 1102 – 4, 12100 = 1102 + 0, 12101 = 1102 + 1, 12102 = 1102 + 2, 12103 = 1102 + 3, 12104 = 1102 + 4, 12144 = 4 • 21 • 41, 12320 = 22 • 130, 12321 = (2 • 31 – 1)2, 12324 = 2 • 3412, 12340 = 4 • 310 – 2, 12342 = 4 • (1 + 2)2 + 3, 12343 = 4 • 32 + 3 + 1, 12344 = 4 • 31 + 4 + 2, 13041 = 1 • 410 – 3, 
, 13044 = (1 + 3)0 + 4 • 4, 13102 = (1 + 1)20 + 3, 13321 = 1132 – 3, 13323 = 32 • (1 + 3)3, 13324 = (3 • (3 • 4 – 1))2, 14111 = 1141 + 1, 14112 = 1142 + 1, 14214 = 4 • 2141, 14330 = 1 • 30 • 34, 20141 = (12 – 1)4 + 0, 20311 = 1 • 213 + 0, 20312 = 213 + 20, 21144 = 4 • 2411, 21232 = –2 + 1232, 21234 = (1 • 2 • 34)2, 21243 = 1232 + 4, 21311 = 2 • (–1 + 311), 21313 = 2 • (13 + 1)3, 21314 = 2 • 143 + 1, 21414 = 24 • 411, 22041 = (2 • 40 – 1)2, 22314 = 21 • (3 • 4)2, 22400 = (2 • 40)2 + 0, 22401 = (2 • 40)2 + 1, 22402 = 2 + (2 • 40)2, 22403 = (2 • 40)2 + 3, 22404 = (2 • 40)2 + 4, 23211 = (132 – 1)2, 
, 23334 = (3 • 4)3 – 32, 23341 = (3 • 4)3 – 12, 23343 = –2 – 3 • (3 • 4)3, 23344 = (23 + 4)3 – 4, 23402 = 223 – 40, 23403 = (23 + 4 + 0)3, 23412 = 223 + 1 • 4, 23434 = (3 • 4)3 + 24, 24024 = (40 + 42)2, 24132 = 31 • 422, 24244 = 424 • 24, 24330 = 4 • 3320, 24343 = 42 • (34 + 3), 24344 = (34 + 44)2, 
, 
, 31042 = 1402 – 3, 31134 = 4 • (133 – 1), 31142 = 23 • 4 – 1 – 1, 31143 = (3 – 1)–1 + 4 • 3, 31144 = 13 • 44 + 1, 31204 = 2 • (410 + 3), 31422 = 221 + 43, 
, 
, 
, 32233 = 3 • (32 • 3 + 2), 
, 32314 = (134 + 3)2, 33204 = (4 • (30 – 3))2, 33222 = 23 • 322, 34021 = 124 – 30, 34041 = (3 + 4)4 – 10, 34042 = (20 – 3)4 – 4, 34043 = (3 + 4)0 + 4 – 3, 34101 = (3 + 4)10 – 1, 34102 = 124 + 30, 34210 = 20 • 31 + 4, 34212 = 34 • 212, 34412 = 124 + 34, 34423 = 4 • ((2 + 3)4 – 3), 40214 = 20 • 44 – 1, 40332 = 2 • (3 + 3)4 + 0, 41122 = 2 • 214 – 1, 43124 = 4 • 143 – 2, 43131 = 4 • 33 • (1 + 1), 43132 = 4 • 33 • 2 + 1, 43134 = 4 • 143 + 3, 43234 = 43 • 23 + 4, 44231 = 3 • (41 + 4 – 2), 44233 = –4 + 42 + 3 • 3, 44242 = 44 • (2 + 4) • 2, 44301 = 3 • 410 + 4, 
, 44314 = 3 • 4 • (44 + 1), 
, 3213 = 32 + 1 + 3, 3214 = 34 + 2 + 1, 3215 = 35 + 1 + 2, 3453 = 5 • 433, 3513 = 51 • 33, 3524 = 33 • 51, 4052 = 502 – 4, 4352 = 45 – 32, 4415 = 44 + 1 – 5, 
, 4431 = 44 + 1 + 3, 4432 = 4 + 43 + 2, 4435 = 45 + 4 + 3, 4452 = 45 + 24, 4504 = 45 + 40, 4515 = 45 + 51, 5204 = 542 + 0, 5325 = 5 • (35 – 2), 5343 = 5 • 34 • 3, 5432 = (54 – 3) • 2, 
, 5532 = 5 • 25 + 3, 10125 = 1012 – 5, 10201 = (100 + 1)2, 10231 = 201 • 31, 10321 = 301 • 21, 10414 = 401 • 14, 10452 = 504 • 12, 11013 = 1031 + 1, 11224 = (112 – 4)2, 11225 = (12 • 5)2 + 1, 11253 = 121 • 53, 11305 = 1301 • 5, 11343 = 141 • 33, 11350 = 1310 • 5, 11513 = 1 • 11 • 35, 11535 = 5 • (1 + 1 + 5)3, 11543 = 5 • 113 + 4, 12004 = 2001 • 4, 12024 = 4012 • 2, 12040 = 2010 • 4, 12042 = 4021 • 2, 12051 = 1102 – 5, 12100 = 1102 + 0, 12101 = 1102 + 1, 12102 = 1102 + 2, 12103 = 1102 + 3, 12104 = 1102 + 4, 12105 = 1102 + 5, 12144 = (12 – 1) • 44, 12204 = 4102 • 2, 12240 = 4120 • 2, 12254 = 4125 • 2, 12321 = (113 – 2)2, 12342 = 242 • 31, 12353 = 3 • (53 + 1 – 2), 12354 = 3 • (54 – 1) – 2, 12400 = 400 • 21, 12402 = 4201 • 2, 12403 = 203 • 41, 12420 = 4210 • 2, 12520 = 50 • 122, 12521 = 2 • 512 – 1, 12522 = (–1 + 25)2 • 2, 12532 = 12 • (35 – 2), 12542 = 4251 • 2, 12544 = 4 • 4 • 152, 
, 13003 = 3001 • 3, 13030 = 3010 • 3, 13053 = 3015 • 3, 13132 = (13 + 1)3 • 2, 13213 = 3 • 231 + 1, 
, 13235 = 215 – 3 • 3, 13242 = (214 – 3) • 2, 13244 = 123 • 4 – 4, 13245 = 1 • 2 • 45 – 3, 13251 = 2 • (1 + 3)5 – 1, 13252 = (–1 + 3)2 • 5 • 2, 13253 = 23+ 3 + 5 + 1, 13254 = 2 • 45 + 3 – 1, 13255 = 25 + 5 + 1 + 3, 13300 = 3100 • 3, 13325 = 215 + 33, 13435 = 53 • 43 – 1, 13452 = 352 + 1 • 4, 13530 = 3150 • 3, 13543 = 13 • (35 – 4), 13553 = 3155 • 3, 14023 = 401 • 23, 14043 = (–1 + 4 + 0)4 + 3, 14121 = (111 + 4)2, 14124 = 221 • 44, 14125 = 1152 + 4, 14230 = 230 • 41, 14250 = 210 • 45, 14252 = 5124 • 2, 14322 = 431 • 22, 14343 = 3 • 3 • (44 – 1), 14344 = 44 • (34 + 1), 14352 = 35 • 142, 14413 = 13 • (44 + 1), 14522 = 5241 • 2, 14523 = 4215 • 3, 15024 = 504 • 21, 15041 = (1 + 5 + 0 + 1)4, 15042 = (5 + 0 + 2)4 + 1, 15134 = 114 + 53, 15204 = 2501 • 4, 15213 = 513 • 21, 15224 = 5412 • 2, 15234 = 5 • 31 • 42, 15240 = 2510 • 4, 15242 = 5421 • 2, 15243 = 2143 • 5, 15303 = 3501 • 3, 15323 = 32 • (53 – 1), 15324 = (–1 + 5) • (3 + 2)4, 15330 = 3510 • 3, 15343 = 3 • 43 • 51, 15344 = 1 • 4 • (54 + 3), 15353 = 3515 • 3, 15404 = 4 • (54 + 10), 15432 = 5 • (123 – 4), 15524 = 2551 • 4, 15533 = 3551 • 3, 15542 = 2 • ((1 + 5)4 – 5), 20412 = 224 – 1 – 0, 21300 = 1302 + 0, 21301 = 1302 + 1, 21302 = 2 + 1302, 21303 = 1302 + 3, 21304 = 1302 + 4, 21305 = 1302 + 5, 21324 = 3221 • 4, 21354 = 314 • 52, 21435 = 2431 • 5, 21455 = 251 • 45, 22120 = 20 • 212, 22245 = 2 • (2 – 2) + 45, 22251 = 52 + 2 + 1 + 2, 22253 = 53 + 2 + 2 + 2, 22255 = 2 + 2 + 2 + 55, 
, 22305 = 52 + 3 + 20, 22355 = 22 • 3 + 55, 22452 = 2 • (2 • 4 • 5)2, 22505 = 55 + 220, 23013 = (31 • 3)2 + 0, 23254 = 22× (35 – 4), 23324 = (2 + 33)2 • 4, 23325 = 233 – 2 • 5, 23333 = 233 – 3 – 3, 23341 = (3 • (4 + 1))3 – 2, 23343 = (2 + 3 • 3 + 4)3, 
, 23345 = (3 • 5)3 + 4 – 2, 
, 23351 = 233 + 5 – 1, 23353 = 2 • 3 + (3 • 5)3, 23424 = 442 • 32, 23514 = 14 • (2 + 5)3, 23550 = 350 • 52, 
, (3 + 4) • 232, 24353 = (3 • 4 • 5)2 – 3, 24513 = 5 • (2 • 4 + 1)3, 24533 = 423 • 35, 25044 = 404 • 52, 25045 = 55 + 402, 25121 = (2 • 51 – 1)2, 25210 = (10 • 5)2 + 2, 25221 = 21 • 252, 25350 = 50 • (53 + 2), 25413 = 413 • 52, 25434 = 2 • 5 • 44 – 2, 
, 25444 = (54 + 44)2, 
, 30541 = 45 + 1 – 3 – 0, 30542 = (3 + 0 + 5)4 – 2, 30543 = (3 + 5)4 – 30, 30544 = ((–3 + 0 + 5) • 4)4, 30545 = (3 + 5)4 + 50, 31155 = 3511 • 5, 31321 = ((3 + 1)3 + 1)2, 31324 = (43 + 1)2 + 3, 32114 = 2 • (311 – 4), 32125 = 2 • 32 + 5 – 1, 32130 = 3 • 2 • 310, 32214 = 2 • (213 + 4), 
, 32441 = (43 + 4 – 1)2, 33213 = 31 • 32 + 3, 33215 = 31 • 35 + 2, 33224 = (34 • 3 + 2)2, 
, 34112 = 2 • (114 – 3), 34120 = 3 • 1042, 34122 = (3 • 2 + 1)4 + 2, 34124 = 2 • ((3 + 4)4 + 1), 34421 = (42 + 1)3 – 4, 34425 = (4 • 2 + 4 + 5)3, 34433 = (33 – 4)3 + 4, 34530 = 4330 • 5, 35052 = (5 • 2)3 • 5 + 0, 35130 = 510 • 33, 35233 = 33 • (35 – 2), 35255 = 535 • 52, 35343 = 35 • (3 + 4) • 3, 35405 = –3 + 5 • 40 + 5, 35412 = 1 • (3 + 2) • 45, 35415 = 3 + 5 • 41 • 5, 35421 = (3 + 2) • (45 + 1), 35425 = 5 • 45 + 32, 35513 = 515 • 33, 41345 = 134 – 45, 41354 = 431 • 54, 41453 = 441 • 53, 41525 = 521 • 45, 42013 = (41 • 3)2 + 0, 42420 = 2042 – 4, 43234 = (34 – 4)2 – 3, 43241 = 1 • (34 – 4)2, 43521 = 41 • (35 – 2), 44240 = 40 • (4 • 4)2, 44521 = (4 • 4 • 5 – 1)2, 44531 = 14 • (54 – 3), 45515 = 5 • ((5 + 1)4 – 5), 45532 = 534 • 52, 45551 = 5 • (5 + 1)4 – 5, 50213 = 35 + 0 + 2 + 1, 50233 = 35 + 3 + 20, 51344 = 44 • (35 + 1), 51423 = 315 – 2 – 4, 51430 = (40 – 5)3 – 1, 51431 = (5 • 1 • 4 – 1)3, 51455 = (5 + 1 + 5) • 54, 51514 = 15 • (54 + 1), 52343 = 45 • 32 + 3, 52345 = 45 • 35 + 2, 53141 = 11 • (45 + 3), 53241 = (34 + 5 – 1)2, 53250 = 50 • (35 – 2), 53430 = 5 • 34 • 30, 54123 = (34 + 5)2 – 1, 54124 = ((4 – 1)4 + 5)2, 54212 = 45 • 212, 54320 = 20 • (54 – 3), 54413 = (54 • 4 – 1) • 3, 
, 54432 = 4 • (54 • 3 + 2), 54433 = (54 • 4 + 3) • 3, 55320 = 50 • 25 + 3, 55515 = –5 • 5 + (5 + 1)5, 55542 = (4 + 2)5 – 5 – 5, 55551 = (5 + 15)5 – 5, 
, 2061 = (2 + 1)6 + 0, 2063 = 36 + 2 + 0, 2314 = 412 + 3, 2343 = 4 • (2 • 3)3, 2422 = –2 + 422, 2424 = 424 – 2, 2534 = 432 + 5, 2542 = (45 – 2)2, 2635 = (5 • 2)3 + 6, 2640 = 40 • 62, 2654 = 26 + 4 – 5, 2662 = 26 + 6 – 2, 3354 = 5 • 3 • 34, 3425 = 2 • (54 – 3), 3464 = –34 + 64, 3531 = (3 + 3)5 – 1, 4323 = 3 • (4 • 2)3, 4625 = (64 – 5)2, 5062 = 602 – 5, 
, 5622 = (65 – 2)2, 
, 6265 = 652 – 6
, 527 = 75 – 2, 1133 = 3 • 311, 1205 = 5 • 201, 1250 = 5 • 210, 1326 = 132 • 6, 1327 = 37 – 1 – 2, 1331 = 33 • (1 + 1), 1332 = 1 + 33 • 2, 1356 = 5 • 6 • 31, 1403 = 3 • 401, 1430 = 30 • 41, 1626 = 21 • 66, 1724 = 7 • 214, 2147 = 7 • 241, 2204 = 422 + 0, 2342 = (2 + 3)4 • 2, 2345 = 2 • 54 + 3, 2346 = 3 • 642, 2372 = 32 • 72, 2416 = 64 – 1 • 2, 2534 = (2 + 5)3 • 4, 2544 = 5 • 424, 2570 = 70 • 52, 2642 = 462 – 2, 2644 = 464 – 2, 
, 2754 = 472 – 5, 3245 = 35 • 34, 3275 = 5 • (73 + 2), 3534 = 3 • (54 + 3), 4213 = 34 + 2 + 1, 4217 = 4 + (2 + 1)7, 4237 = 37 + 24, 4334 = 34 • 34, 4527 = 74 – 5 • 2, 4534 = (3 + 4)4 – 5, 4537 = 74 – 5 + 3, 4541 = (14 – 5)4, 4572 = 74 + 52, 4576 = 5 • 746, 4654 = 4 • (–6 + 54), 5374 = 54 + 37, 5676 = 6 • 765, 5726 = 672 + 5, 6065 = (–60 + 6)5, 6072 = 702 – 6, 7246 = (7 – 2)4 • 6
, 2737 = –27 + 37, 3254 = –3 + (2 + 5)4, 3247 = 74 – 32, 3257 = 75 + 2 – 3, 3454 = 5 • (4 + 4)3, 3458 = 5 • 83 + 4, 3672 = (2 • 7)3 – 6, 3678 = (7 • (8 – 6))3, 4126 = 612 – 4, 
, 4357 = 37 + 45, 5485 = 84 – 55, 6280 = 80 • 26, 6827 = 782 + 6, 7082 = 802 – 7, 8836 = 38 – 6 • 8, 8873 = 38 – 7 – 8
, 1395 = 15 • 93, 1435 = 35 • 41, 1503 = 3 • 501, 1530 = 3 • 510, 1792 = 7 • 29 – 1, 1827 = 21 • 87, 
, 2187 = (2 + 18)7, 2349 = 29 • 34, 2500 = 502 + 0, 2501 = 502 + 1, 2502 = 2 + 502, 2503 = 502 + 3, 2504 = 502 + 4, 2505 = 502 + 5, 2506 = 502 + 6, 2507 = 502 + 7, 2508 = 502 + 8, 2509 = 502 + 9, 2592 = 25 • 92, 2737 = (2 • 7)3 – 7, 2916 = (1 • 6 • 9)2, 3125 = (3 + 1 • 2)5, 3159 = 9 • 351, 
, 3375 = (3 + 5 + 7)3, 3378 = (7 + 8)3 + 3, 3685 = (36 + 8) • 5, 3784 = 8 • 473, 3864 = 3 • (– 8 + 64), 3972 = 3 + (9 • 7)2, 4088 = 84 – 8 – 0, 4096 = (4 + 0 • 9)6, 4106 = 46 + 10, 4167 = 46 + 71, 4536 = 56 • 34, 4624 = (64 + 4)2, 4628 = 682 + 4, 5120 = 5 • 210, 5776 = 767 – 5, 5832 = (2 • 5 + 8)3, 6144 = 6 • 44 + 1, 6145 = 6 • 45 + 1, 6455 = (64 – 5) • 5, 6880 = 8 • 860, 7928 = 892 – 7, 8092 = 902 – 8, 8192 = 8 • 29 + 1, 9025 = 952 + 0, 9216 = 1 • 962, 9261 = 219 – 6, 10192 = 1012 – 9, 10201 = 1012 + 0, 10251 = 51 • 201, 10255 = 5 • 2051, 10368 = 8 • 61 + 0 + 3, 10426 = 26 • 401, 10521 = 21 • 501, 10525 = 5 • 2105, 10575 = 15 • 705, 10824 = 1042 + 8, 10935 = 15 • 93 + 0, 11025 = (110 – 5)2, 11163 = 3 • 611 + 1, 11259 = 9 • 1251, 11264 = 11 • 26 + 4, 11439 = 9 • 31 • 41, 11663 = 16 • 36 – 1, 
, 
, 11844 = 84 • 141, 11848 = 8 • 1481, 11943 = 9 • (113 – 4), 12006 = 6 • 2001, 12060 = 6 • 2010, 12091 = 1102 – 9, 12100 = 1102 + 0, 12101 = 1102 + 1, 12102 = 1102 + 2, 12103 = 1102 + 3, 12104 = 1102 + 4, 12105 = 1102 + 5, 12106 = 1102 + 6, 12107 = 1102 + 7, 12108 = 1102 + 8, 12109 = 1102 + 9, 12167 = (16 + 7)1 + 2, 
, 12321 = (113 – 2)2, 12337 = 73 • 132, 12384 = 3 • 4128, 12493 = (4 + 9) • 312, 12505 = 5 • 2501, 12544 = (51 – 2) • 44, 12546 = 51 • 246, 12550 = 5 • 2510, 12595 = 5 • 2519, 12600 = 6 • 2100, 12762 = 6 • 2127, 12768 = 8 • 21 • 76, 12769 = (96 + 17)2, 12798 = 2 • 79 • 81, 12802 = 2 • (802 + 1), 12843 = 3 • 4281, 12850 = (1 + 28) • 50, 12955 = 5 • 2591, 12960 = 160 • 92, 12964 = 14 • 926, 12996 = (6 • (1 + 9 + 9))2, 13125 = 21 • 53 + 1, 13176 = 61 • (7 – 1)3, 13225 = (1 • 5 • 23)2, 13286 = 26 • (83 – 1), 13243 = 41 • 323, 13496 = 4 • ((6 + 9)3 – 1), 13545 = 3 • 4515, 13689 = (9 • 13)8 – 6, 13725 = 5 • ((2 • 7)3 + 1), 13764 = 6 • 31 • 74, 13813 = (3 • 8)3 – 11, 13822 = (3 • 8)2 + 1 – 2, 13823 = (3 • 8)3 – 2 + 1, 13824 = (3 • 8)4 + 1 – 2, 13825 = 1 + (3 • 8)–2 + 5, 13826 = (18 + 6)3 + 2, 13832 = (3 + 21)3 + 8, 13842 = 243 + 18, 13950 = 15 • 930, 14035 = 35 • 401, 14129 = 114 – 29, 14168 = 11 • (64 – 8), 14175 = 7 • 451 + 1, 14256 = (2 • 5 + 1) • 64, 14350 = 35 • 410, 14352 = 23 • (54 – 1), 14641 = (1 + 4 + 6)4 • 1, 14645 = (5 + 6)4 + 4 • 1, 14647 = (4 + 7)4 + 6 • 1, 15003 = 3 • 5001, 15030 = 3 • 5010, 15125 = 5 • (5 • 11)2, 15246 = 6 • 2541, 15300 = 3 • 5100, 15345 = 3 • 5 • (45 – 1), 15378 = 7 • (5 + 8)3 – 1, 15379 = 7 • (5 + 9 – 1)3, 15435 = 3 • 5145, 15495 = 15 • (45 + 9), 15552 = (15 + 5)5 • 2, 15562 = 1 • 2 • (65 + 5), 15567 = 56 – 57 – 1, 15568 = 56 – 58 + 1, 15585 = 1 • (55 – 8) • 5, 15586 = 56 – 5 • 8 + 1, 15612 = –1 + 56 – 12, 15613 = 1 + 56 – 13, 15615 = 56 – 5 • (1 + 1), 15617 = –1 + 56 – 1 • 7, 15618 = 1 + 56 – 1 • 8, 
, 15621 = –1 + 56 – 2 – 1, 15622 = 1 + 56 – 2 – 2, 15623 = –1 + 56 + 2 – 3, 15624 = 1 + 56 + 2 – 4, 15625 = 56 • 125, 15626 = 1 + 56 • 2 – 6, 15627 = 56 + 2 • 17, 15628 = 56 + 8 / 2 – 1, 
, 15631 = 56 + (1 + 1) • 3, 15632 = 1 + 56 + 3 • 2, 15633 = –1 + 56 + 3 • 3, 15634 = 56 + 13 – 4, 15635 = 56 + 5 • (3 – 1), 15641 = 56 + 41 + 1, 15642 = 1 + 56 + 42, 15645 = 1 • 56 + 4 • 5, 15655 = 1 • 5 • (6 + 55), 15656 = 1 + 56 + 5 • 6, 15661 = 56 + 61 + 1, 15662 = 1 + 56 + 62, 15667 = 1 • 56 + 6 • 7, 15679 = 56 + 9 • (7 – 1), 15688 = –1 + 56 + 8 • 8, 15689 = 56 + 8 • (9 – 1), 15697 = 56 + 9 • (7 + 1), 15698 = 1 + 56 + 9 • 8, 15795 = 9 • 1755, 15975 = 5 • 5 • 9 • 71, 16225 = 6 • 522 + 1, 16245 = 5 • (61 – 4)2, 16272 = 6 • 2712, 16295 = (1 + 6)5 – 29, 16347 = 47 – 36 – 1, 16348 = 48 – 1 – 36, 16368 = 8 • 31 • 66, 16372 = (1 + 3)7 – 6 • 2, 16374 = 47 – 1 – 6 – 3, 16375 = (5 – 1)7 – 6 – 3, 16377 = (1 + 6 – 3)7 – 7, 16378 = (8 – 3 – 1)7 – 6, 16381 = (1 + 1)6 + 8 – 3, 16382 = (3 – 1)6 + 8 – 2, 16384 = 163 • (8 – 4), 16385 = (5 – 3)6 + 8 + 1, 
, 16447 = –1 + 64 + 47, 16448 = 48 – 1 + 64, 16479 = 47 + 96 – 1, 16743 = 76 – 1 – 43, 16758 = 75 – 6 • 8 – 1, 16759 = 75 – 6 • (9 – 1), 16765 = 75 – 6 • (6+1), 16783 = 76 – 1 – 8 • 3, 16794 = 76 – 1 – 9 – 4, 
, 
, 16807 = 76 – 1 + 0 • 8, 16815 = (1 + 6)5 + 1 • 8, 16875 = 1 • 68 + 75, 16879 = 76 – 1 + 8 • 9, 17253 = (72 – 1) • 35, 17325 = 75 • 231, 17328 = 8 • (37 – 21), 17346 = 6 • 7 • 413, 17368 = 8 • (37 – 16), 17384 = 8 • (37 – 14), 17428 = 2 • 8714, 17437 = 47 • 371, 17482 = 2 • 8741, 17488 = 8 • (4 – 1)7 – 8, 17536 = 1 + 75 + 36, 17689 = (7 • 19)8 – 6, 
, 17892 = 9 • 28 • 71, 17920 = 70 • 29 – 1, 17925 = 5 • (7 • 29 + 1), 18225 = 81 • 225, 18265 = 65 • 281, 18270 = 21 • 870, 18432 = 18 • 43 + 2, 18435 = 18 • 45 + 3, 18522 = 2 • 218 – 5, 18594 = 18 • (45 + 9), 18723 = 3 • (71 + 8)2, 18744 = 71 • (44 + 8), 19026 = 21 • 906, 19215 = 21 • 915, 19321 = 1 • 1392, 19392 = 39 – 291, 19453 = 19 • 45 – 3, 19592 = (5 – 2)9 – 91, 19629 = (1 + 2)9 – 6 • 9, 
, 19653 = 39 – 1 • 5 • 6, 
, 19683 = 1 • (9 – 6)8 • 3, 
, 
, 19693 = (6 – 3)9 + 1 + 9, 19732 = 39 + 1 • 72, 19734 = 3 • (94 + 17), 19736 = 9 • (37 + 6) – 1, 19737 = 9 • (37 + 7 – 1), 19738 = 39 + 7 • 8 – 1, 19739 = (–1 + 9) • 7 + 39, 19773 = 9 • (7 + 7 – 1)3, 19845 = 5 • 49 • 81, 20485 = 5 • (20 + 84), 20736 = (2 • 6)7 – 3 + 0, 21175 = 7 • (5 • 11)2, 21375 = 3 • 7125, 21495 = 21 • 45 – 9, 21504 = 21 • 45 + 0, 21586 = 86 • 251, 21606 = 6 • (602 + 1), 21753 = 3 • 7251, 
, 
, 
, 
, 21870 = 27 • 810, 21875 = 7 • (8 – 2 – 1)5, 21943 = (2 • 14)3 – 9, 21952 = (29 – 1)5 – 2, 21953 = (2 • (5 + 9))3 + 1, 22264 = 46 • 222, 
, 22757 = 7 • (572 + 2), 23326 = 3 • 62 + 3 – 2, 23328 = (2 • 33)2 • 8, 23392 = 32 • (93 + 2), 23456 = 25 • (36 + 4), 23490 = 290 • 34, 23546 = 23 • 45 – 6, 23548 = (3 + 4) • 582, 23552 = 23 • 25 + 5, 23796 = 6 • (632 – 3), 24336 = (4 • (36 + 3))2, 24339 = (4 • 39)2 + 3, 24367 = 7 • (63 – 4)2, 24375 = (37 + 2) • 54, 
, 24389 = (2 • 8 + 9 + 4)3, 24390 = 293 + 40, 24393 = (3 • 9 + 2)3 + 4, 24546 = (2 + 4) • (–5 + 46), 24564 = 6 • (4 • 45 – 2), 24566 = 6 • 46 – 2 • 5, 
, 24584 = 24 • 45 + 8, 24586 = 6 • 84 + 2 • 5, 24768 = 4 • 72 • 86, 24964 = (94 + 64)2, 24972 = 4 • (792 + 2), 25105 = 5 • 5021, 25137 = 513 • 72, 
, 25375 = 35 • 725, 25474 = 47 • 542, 25510 = 5 • 5102, 25725 = 525 • 72, 25872 = 528 • 72, 25895 = 5 • ((8 • 9)2 – 5), 25921 = (159 + 2)2, 26238 = 2 • 2 • 38 – 6, 
, 26348 = 4 • (38 + 26), 
, 26496 = 9 • 46 • 26, 26624 = 26 • 24 + 6, 26754 = 546 • 72, 26896 = (96 + 68)2, 
, 
, 27634 = 2 • ((6 • 4)3 – 7), 27639 = 27 • 63 – 9, 
, 27653 = 63 • 27 + 5, 27654 = 27 • 45 + 6, 
, 27889 = (79 + 88)2, 28217 = (21 • 7)2 – 7, 28224 = (2 + 82)2 • 4, 28226 = (28 • 6)2 + 2, 
, 28476 = 7 • (46 – 28), 28547 = (8 + 5)4 – 7 • 2, 28554 = (8 + 5)4 – 5 – 2, 28556 = (8 + 5)6 – 2 – 5, 28559 = –2 + (8 + 5)–5 + 9, 28561 = 1 • (8 + 5)6 – 2, 
, 
, 28672 = 7 • (8 – 2 – 2)6, 28674 = 7 • (8 – 4)6 + 2, 28678 = 7 • (8 • 8)2 + 6, 28728 = 7 • (82 • 2 + 8), 28749 = 7 • (84 + 9 + 2), 28764 = 6 • (2 • 74 – 8), 28784 = 7 • (84 + 16), 28900 = (80 + 90)2, 29160 = 10 • (6 • 9)2, 29184 = 4 • 8 • 912, 
, 
, 
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, 
, 
, 
, 
, 
, 
, 29584 = (4 • 5 • 9 – 8)2, 29632 = 32 • 926, 29768 = 8 • (9 • 6 + 7)2, 29795 = 59 • (29 – 7), 29929 = (9 • 9 + 92)2, 30625 = (3 • 60 – 5)2, 31250 = 10 • (2 + 3)5, 31252 = 2 • (52 • 3 + 1), 31256 = 1 • 2 • (56 + 3), 31346 = 43 • 36 – 1, 31347 = 43 • 37 – 1, 31509 = 9 • 3501, 31590 = 9 • 3510, 31682 = 62 • (83 – 1), 32685 = (6 + 2)5 – 83, 32697 = 63 • (29 + 7), 32744 = 2 • (47 – 3 • 4), 32747 = 2 • 47 – 3 • 7, 32751 = 23 • 5 – 17, 32759 = (3 – 2 + 7)5 – 9, 32761 = 23 • (6 – 1) – 7, 32762 = 23 • (7 – 2) – 6, 32764 = 23 • 7 – 6 – 4, 32765 = –3 + (2 • 7 – 6)5, 
, 32771 = 3 + 27 + 7 + 1, 32772 = 2 • ((7 – 3)7 + 2), 32775 = (7 + 3 – 2)5 + 7, 32778 = 27 + 8 + 7 + 3, 32781 = 27 + 8 + 13, 32782 = 83 + 2 + 7 • 2, 32783 = 323 + 7 + 8, 32785 = 3 + 2 • 7 + 85, 32786 = 27 + 8 + 3 • 6, 32795 = 5 • (97 – 3 – 2), 32805 = 5 • (38 + 2 • 0), 32815 = 5 • (38 + 2 • 1), 32825 = 5 • (38 + 2 • 2), 32832 = 323 + 82, 32835 = 5 • (38 + 2 • 3), 32836 = 323 + 68, 32845 = 5 • (38 + 2 • 4), 32849 = 323 + 92, 32851 = 215 + 83, 32853 = 323 + 85, 32854 = 85 + 43 • 2, 32855 = 5 • (38 + 2 • 5), 32859 = 85 + 93 – 2, 32865 = 5 • (38 + 2 • 6), 32875 = 5 • (38 + 2 • 7), 32885 = 5 • (38 + 2 • 8), 32895 = 5 • (38 + 2 • 9), 33495 = 33 • (45 – 9), 33579 = 7 • 9 • 533, 33655 = 53 • 635, 33696 = 36 • 936, 34425 = 34 • 425, 34968 = 3 • (9 • 64 – 8), 34986 = 48 • 93 – 6, 
, 
, 
, 34996 = 6 • (9 + 9)3 + 4, 35152 = 2 • (5 • 5 + 1)3, 35684 = 85 – 4 • 36, 35721 = 35 • 7 • 21, 35726 = 72 • 36 + 5, 
, 35928 = (52 + 8)3 – 9, 35932 = (3 • (9 + 2))3 – 5, 35933 = 333 + 5 – 9, 35937 = (35 + 7 – 9)3, 35942 = (42 – 9)3 + 5, 
, 36549 = 9 • (46 – 35), 36850 = (36 + 8) • 50, 36855 = 63 • 585, 36864 = (6 + 6 – 3) • 84, 36918 = 9 • (83 + 1 + 6), 37179 = 37 • (1 + 7 + 9), 37187 = 17 • 37 + 8, 37249 = (3 • 7 • 9 + 4)2, 
, 37668 = 6 • 73 • 86, 37814 = 74 • (83 – 1), 37840 = 8 • 4730, 37845 = 87 • 435, 37875 = 75 • (83 – 5), 
, 38424 = (2 • (3 + 4))4 + 8, 38427 = (2 • 7)4 + 8 + 3, 38637 = (8 • 7 – 3) • 36, 38640 = 30 • (–8 + 64), 38856 = (38 – 85) • 6, 38912 = 38 • 29 + 1, 
, 39283 = 39 • 2 – 83, 39288 = 8 • ((9 + 8)3 – 2), 39294 = 2 • (39 – 36), 39295 = (52 + 9)3 – 9, 39304 = 343 + 0 • 9, 39313 = (33 + 1)3 + 9, 39314 = 343 + 1 + 9, 39328 = 2 • 39 – 38, 39342 = (39 – 3 • 4) • 2, 39343 = 39 + 343, 
, 39358 = 39 • (–3 + 5) – 8, 
, 
, 
, 
, 39369 = 3 + 93 • 6 • 9, 39372 = (3 + 9 • 37) • 2, 39382 = ((3 • 9)3 + 8) • 2, 39424 = 29 • (34 – 4), 39456 = 6 • (94 + 3 • 5), 39784 = 8 • 4973, 39864 = 6 • (94 + 83), 39945 = 39 • 45 + 9, 41323 = 43 • 312, 41468 = 4 • (8 • 64 – 1), 41472 = 2 • (1 + 4 + 7)4, 41665 = 641 • 65, 42025 = 2054 – 2, 42336 = 6 • (34 + 3)2, 42875 = (42–7)8 – 5, 42898 = 89 • 482, 43264 = (63 – 4 – 4)2, 43268 = (63 – 8)2 + 4, 43375 = 53 • (73 + 4), 43688 = 86 • (83 – 4), 
, 
, 
, 43775 = (4 • 37 + 7) • 5, 43932 = 3 • ((9 + 2)3 + 3), 44375 = 54 • (43 + 7), 44676 = 6 • 7446, 44977 = (7 + 7)4 + 94, 45056 = (50 – 6) • 45, 45360 = 35 • 64 + 0, 45361 = 35 • 64 + 1, 45362 = 35 • 64 + 2, 45363 = 35 • 64 + 3, 45364 = 35 • 64 + 4, 45365 = 35 • 64 + 5, 45366 = 35 • 64 + 6, 45367 = 35 • 64 + 7, 45368 = 35 • 64 + 8, 45369 = 35 • 64 + 9, 45632 = –45 + 63 • 2, 45684 = 54 • 846, 45760 = 65 • 704, 45864 = 84 • 546, 45873 = 7 • 38 – 54, 45927 = ((4 + 5) • 9)2 • 7, 45947 = 4 • 5 + 94 • 7, 45957 = 7 • (94 + 5) – 5, 45978 = 7 • (94 + 8) – 5, 46256 = 66 – (4 • 5)2, 46368 = 36 • (64 – 8), 46556 = 66 – 4 • 5 • 5, 46593 = 3 • (56 – 94), 46608 = 66 – 48 + 0, 46613 = 66 – 43 • 1, 46615 = 6 • 6
, 46649 = 66 – 4 • 4 + 9, 46650 = 66 – 5 – 40, 46651 = –4 + 6 • 65 – 1, 46652 = –4 + (6 • 6)5 – 2, 
, 46655 = 4 + 6 • 65 – 5, 46656 = (–4 • 6 + 6 • 5)6, 
, 
, 46660 = 4 + 66 + 6 • 0, 46661 = 66 + 4 + 16, 46662 = 62 • 64 + 6, 46663 = 4 + 66 + 6 – 3, 46664 = 66 + 4 • (6 – 4), 
, 
, 
, 46673 = –4 + 66 + 7 • 3, 46677 = 66 + 4 • 7 – 7, 46684 = –4 + 66 + 8 • 4, 
, 46691 = 66 + 4 • 9 – 1, 46851 = (4 – 1) • (56 – 8), 46875 = (4 + 7 – 8) • 56, 47538 = 57 • 834, 47652 = 76 • (54 + 2), 48672 = 78 • 624, 48750 = 78 • 54 + 0, 48751 = 78 • 54 + 1, 48752 = 78 • 54 + 2, 48753 = 78 • 54 + 3, 48754 = 78 • 54 + 4, 48755 = 78 • 54 + 5, 48756 = 78 • 54 + 6, 48757 = 78 • 54 + 7, 48758 = 78 • 54 + 8, 48759 = 78 • 54 + 9, 49152 = (4 – 1) • 29 + 5, 49277 = 9 • 742 – 7, 49584 = 48 • (45 + 9), 49855 = 59 • 845, 49896 = 6 • 84 • 99, 49968 = 8 • 9 • 694, 51200 = 50 • 210, 
, 51759 = 9 • 5751, 52168 = 8 • 6521, 
, 52483 = 2 • 4 • 38 – 5, 52488 = (5 + 2 – 4)8 • 8, 52493 = 23 • 94 + 5, 52498 = 8 • 94 + 2 • 5, 52731 = 217 • 35, 
, 53245 = 52 • 45 – 3, 53248 = 52 • 48 – 3, 53297 = 2 • 75 + 39, 53824 = (8 • (34 – 5))2, 53865 = 63 • 855, 54369 = (3 + 4) • (65 – 9), 54378 = 87 • 54 + 3, 54432 = (4 + 3) • (4 + 2)5, 54436 = (4 + 3) • 65 + 4, 54476 = 7 • 65 + 44, 54642 = 42 • (64 + 5), 54726 = 7 • (65 + 42), 54768 = 7 • (65 + 48), 54872 = (8 • 5 – 2)7 – 4, 54953 = 95 – (3 + 5)4, 54958 = 95 – 84 + 5, 55225 = (5 • (52 – 5))2, 55296 = 54 • 210, 56295 = 9 • 6255, 56628 = (5 + 8) • 662, 56732 = 26 • (37 – 5), 56875 = 65 • 875, 57288 = 8 • (25 + 8 – 7), 57644 = 4 • (6 • 74 + 5), 57645 = 57 – 5 • 46, 58921 = 95 – 28 – 1, 58957 = 95 – 87 –5, 58971 = 95 – 78 • 1, 58973 = 95 – 83 + 7, 58978 = 95 – 8 • 8 – 7, 59032 = 95 – 20 + 3, 59038 = 95 – 8 – 3 – 0, 59039 = 95 – 9 – 30, 59044 = 95 – 4 – 40, 59045 = 95 – 4 – 0 • 5, 59046 = 95 – 4 + 60, 59048 = 95 – 480, 59049 = 95 + 0 • 4 • 9, 59050 = 95 + 50 + 0, 59051 = 95 + 50 + 1, 59052 = 5 + 90 + 5 – 2, 59053 = 95 + 50 + 3, 59054 = 95 + 50 + 4, 59055 = 95 + 50 + 5, 59056 = 95 + 50 + 6, 59057 = 95 + 50 + 7, 59058 = 95 + 50 + 8, 59059 = 95 + 50 + 9, 
, 59094 = 9 • (94 + 1) + 0, 59128 = 95 + 81 – 2, 59129 = 95 + 92 – 1, 59147 = 95 + 7 • 14, 59263 = 95 + 63 – 2, 59265 = 95 + 65 – 2, 59273 = 95 + 7 • 32, 59313 = 393 – 5 – 1, 59314 = 394 – 1 – 5, 59318 = 398 – 5 – 1, 59319 = 399 – 5 – 1, 59375 = (9 + 3 + 7) • 55, 59392 = 95 + (9 – 2)3, 59409 = 95 + 4 • 90, 59451 = 19 • (55 + 4), 
, 61435 = 5 • (3 • 64 – 1), 61440 = 60 • 44 + 1, 62476 = 6 • ((7 – 2)6 – 4), 
, 62504 = 4 • (56 + 20), 62564 = 4 • 56 + 26, 62968 = 68 • 926, 63478 = 48 – 6 • 73, 63895 = 65 • 983, 63904 = 403 – 96, 63945 = 63 • (–9 + 45), 63985 = (8 • 5)3 – 6 – 9, 63994 = (49 – 9)3 – 6, 64036 = 403 + 6 • 6, 64512 = 45 • (26 – 1), 64513 = 63 • 45 + 1, 64522 = 2542 + 6, 64550 = (64 – 5) • 50, 64868 = 48 – 668, 65344 = 64 • (45 – 3), 65471 = –65 + 47 + 1, 65478 = 48 – 65 + 7, 65480 = 48 – 56 + 0, 65481 = 48 – 56 + 1, 65482 = 48 – 56 + 2, 65483 = 48 – 56 + 3, 65484 = 48 – 56 + 4, 65485 = 48 – 56 + 5, 65486 = 48 – 56 + 6, 65487 = 48 – 56 + 7, 65488 = 48 – 56 + 8, 65489 = 48 – 56 + 9, 65491 = 169 – 5 – 45, 65528 = 25 + 5 + 6 – 8, 65531 = (5 – 3)16 – 5, 
, 65542 = 45 + 5 – 2 + 6, 65841 = 48 + 5 • 61, 65884 = 48 + 6 • 58, 66339 = (6 • 6)3 + 39, 66554 = 65 • 45 – 6, 67149 = 9 • 7461, 67228 = 28 • 76 – 2, 67234 = 6 + 72 + 3 • 4, 67252 = 2 • 2 • (75 + 6), 67254 = 4 • (75 + 6) + 2, 67392 = 72 • 936, 67950 = 75 • 906, 68644 = (44 + 6)8 – 6, 68800 = 8 • 8600, 69253 = 95 • 36 – 2, 69255 = 95 • (5 – 2)6, 
, 69822 = 862 • 92, 69895 = 9 • (65 – 9) – 8, 
, 
, 69985 = 9 • 65 + 9 – 8, 69993 = 96 • 93 + 9, 70225 = (270 – 5)2, 71199 = 9 • 7911, 72576 = 567 • 27, 73125 = 13 • 752, 73926 = 6 • 9 • 372, 73984 = (8 • 34)9 – 7, 74183 = 31 • (74 – 8), 74353 = 34 • 37 – 5, 74358 = 34 • (8 – 5)7, 74533 = 73 • (45 – 3), 74536 = 56 • (4 + 7)3, 74892 = (4 + 8) • 792, 
, 75433 = 47 + (3 • 3)5, 76335 = 35 • (37 – 6), 76832 = 2 • (6 + 8)7 – 3, 
, 77459 = 57 – 9 • 74, 
, 78115 = 57 – 8 – 1 – 1, 78116 = (6 – 1)7 – 8 – 1, 78117 = (6 – 1)7 – 8 • 1, 78123 = (8 – 3)7 – 2 • 1, 78125 = 57 • 182, 
, 78132 = (2 + 3)7 + 8 – 1, 78133 = (3 + 3 – 1)7 + 8, 78135 = 57 + 8 + 3 – 1, 78136 = (6 – 1)7 + 8 + 3, 78152 = 57 + 28 – 1, 78163 = (6 – 1)7 + 38, 78165 = 57 + 8 • (6 – 1), 78225 = 57 + (2 + 8)2, 78545 = 57 + 5 • 84, 78605 = 57 + 6 • 80, 78659 = 57 + 6 • 89, 78732 = (7 + 7 – 2) • 38, 78975 = 9 • 8775, 79299 = 92 • 979, 81225 = 1 • 2852, 81648 = (8 • 8 – 1) • 64, 81920 = 80 • 29 + 1, 82372 = 2872 + 3, 82755 = 5 • (75 – 28), 82936 = (3 • 96)2 – 8, 82942 = (4 • 8 • 9)2 – 2, 
, 82952 = (9 • 25)2 + 8, 83357 = 73 • 35 + 8, 83521 = (25 – 8)3 + 1, 83524 = (25 – 8)4 + 3, 83957 = 57 + 8 • 93, 
, 84672 = 48 • (6 • 7)2, 85264 = (4 • (68 + 5))2, 85293 = (2 • 9 – 5) • 38, 85358 = (5 + 8) • (38 + 5), 86142 = 21 • (84 + 6), 86724 = (74 + 8) • 62, 
, 
, 91125 = (9 • 5 • 1)2 + 1, 91853 = (9 + 5) • 38 – 1, 91854 = (9 + 5) • (4 – 1)8, 92160 = 10 • 962, 93184 = 91 • 48 – 3, 93217 = 97 • 312, 93294 = 2 • ((4 • 9)3 – 9), 93312 = 2 • (9 • (3 + 1))3, 93642 = (9 • 34)2 + 6, 94395 = 93 • (45 – 9), 95232 = 93 • 22 • 5, 95234 = 93 • 45 + 2, 97333 = (39 + 7)3 – 3, 97336 = (39 + 7)6 – 3, 97343 = (49 – 3)3 + 7, 97375 = 779 • 53, 97966 = 76 – (9 – 6)9, 98256 = 6 • (29 + 5 – 8), 98304 = 3 • 89 – 4 + 0, 98305 = 3 • 85 + 90, 98325 = 3 • (85 + 9 – 2), 98375 = 5 • (9 • 37 – 8), 98415 = 98 – 4 • 15, 98435 = 5 • (39 + 8 – 4), 99225 = ((9 – 2) • 9 • 5)2
, 2B36 = 326 • B, 3166 = 631 • 6, 3266 = 63 • 62, 
, 3548 = 834 • 5, 35A6 = 6 • (A3 + 5), 3760 = 730 • 6, 37B6 = 73B • 6, 
, 3B76 = 7B3 • 6, 416B = 461 • B, 45A8 = 548 • A, 46A8 = 6A4 • 8, 47BA = 4A • B7, 4892 = 2 • (84 – 9), 48A8 = (A – 2) • 84, 4969 = 649 • 9, 5513 = 55 • 1 • 3, 5788 = 857 • 8, 57BA = 75 • B • A, 
, 597B = 9B5 • 7, 5B14 = (11 – 1) • 45, 5B22 = 2B + 2 • 5, 6946 = 9 • (64 + 6), 
, 7A28 = 8A • 27, 95A2 = 29 + 5 + A, 9B2A = AB2 + 9, A0B2 = B02 – A, A454 = 5A • 44, BA24 = A • 2B – 4
, 1623 = 12 • 63, 173A = 73 • A – 1, 173B = 73 • (B – 1), 1829 = (8 – 1) • 29, 1B27 = 2B + 1 – 7, 1B31 = (3 – 1)B + 1, 1B3C = (3 – 1)C + B, 22B8 = 28 • B2, 2370 = 30 • 27, 248A = (4 • (8 + A))2, 24A0 = 40 • A2, 256B = B5 • 62, 2653 = (56 + 3)2, 2659 = 592 + 6, 
, 
, 2A3B = 2B • 3 – A, 2CA9 = (C – 9)A – 2, 31B9 = 39 • B1, 3845 = (5 • (8 – 4))3, 3C24 = (34 + C)2, 3C25 = (C3 + 2) • 5, 3C5B = C3 + 5 • B, 3C96 = 93 • C – 6, 3CA9 = 93 • C + A, 426C = ((C + 4) • 6)2, 4719 = (9 + 1)4 – 7, 471A = (A + 7 – 1)4, 5682 = 862 + 5, 7155 = 55 + 1 – 7, 7156 = 57 – 1 – 6, 715C = (C – 7)5 + 1, 7165 = 56 + 7 – 1, 7166 = 7 + (–1 + 6)6, 75C4 = (7 – 5)C • 4, 77C5 = 75 – 7 • C, A3B7 = (A + 7) • B3, AC2B = BC2 + A, B0C2 = C02 – B
, 1196 = (1 + 1)9 • 6, 11B6 = 16 • B6, 1208 = 201 • 8, 126A = 2A • 61, 1280 = 21 • 80, 1324 = (43 – 1)2, 1350 = 10 • 35, 1356 = 36 • 51, 1375 = 371 • 5, 137A = 73 • A + 1, 1440 = 10 • 44, 1447 = 41 • 47, 1452 = (45 – 1)2, 1488 = 41 • 8 • 8, 14AC = 1C4 • A, 16C2 = 1 • 2C – 6, 16C8 = 1 • (8 – 6)C, 1703 = 701 • 3, 1730 = 71 • 30, 1832 = (18 • 3)2, 1B84 = 41 • B • 8, 1C29 = C9 • 21, 1C83 = 8C1 • 3, 218C = 182 • C, 21A8 = (A + 8)2 + 1, 234C = (2 • 4)3 • C, 2408 = 802 • 4, 2480 = 40 • 82, 2569 = (–2 + 5)6 • 9, 2880 = 82 • 80, 2940 = 90 • 42, 29A4 = (9 • A – 4)2, 
, 2B37 = B3 • 72, 2D65 = D • 56 – 2, 2D93 = 2D – 9 • 3, 2DA3 = 2D – A + 3, 2DAD = 2D + A – D, 2DB1 = 2D – 1B, 2DC0 = 2D + C + 0, 2DC1 = 2D + C + 1, 2DC2 = 2D + C + 2, 2DC3 = 2D + C + 3, 2DC4 = 2D + C + 4, 2DC5 = 2D + C + 5, 2DC6 = 2D + C + 6, 2DC7 = 2D + C + 7, 2DC8 = 2D + C + 8, 2DC9 = 2D + C + 9, 2DCA = 2D + C + A, 2DCB = 2D + C + B, 2DCC = 2D + C + C, 2DCD = 2D + C + D, 2DD1 = 2D + 1D, 328C = 38 – 2 • C, 378C = (C + 7) • 83, 384C = C83 • 4, 38D2 = 3 • D • 28, 3904 = (30 + 9)4, 415B = (45 – 1) • B, 458C = C48 • 5, 
, 517D = 571 • D, 5962 = (65 + 9) • 2, 59B7 = B59 • 7, 5B97 = B95 • 7, 61A7 = 76 – 1A, 7645 = (46 – 7) • 5, 8A2C = A28 • C, 91AC = A91 • C, 997B = B99 – 7, A929 = ((A + 9) • 9)2, BD2C = CD2 + B, C0D2 = D02 – C, D32C = 3D2 • C
, 1144 = 411 • 4, 11AA = 1A1 • A, 1214 = 421 + 1, 1235 = 21 • 53, 12B3 = (1 + 2) • B3, 12DA = 21 • A • D, 12DC = 1D • C2, 1306 = 301 • 6, 132C = 2C + 3 – 1, 1360 = 31 • 60, 1469 = 94 – 1 • 6, 1504 = 501 • 4, 152A = A15 • 2, 1540 = 51 • 40, 15A2 = A51 • 2, 163E = 6E • 31, 17A3 = (A – 1)3 • 7, 192A = 91 • 2A, 1DB3 = D1 • B • 3, 1E26 = (1 + 2)E – 6, 
, 2486 = (8 – 2)4 • 6, 24A8 = 8A2 • 4, 252E = 5E2 – 2, 2585 = (5 • 8)2 • 5, 258D = 52 • 8 • D, 2600 = 602 + 0, 2601 = 602 + 1, 2602 = 2 + 602, 2603 = 602 + 3, 2604 = 602 + 4, 2605 = 602 + 5, 2606 = 602 + 6, 2607 = 602 + 7, 2608 = 602 + 8, 2609 = 602 + 9, 260A = 602 + A, 260B = 602 + B, 260C = 602 + C, 260D = 602 + D, 260E = 602 + E, 2662 = (–2 + 6)6 • 2, 2757 = (75 + 7) / 2, 28C6 = 8C2 • 6, 2B87 = B2 • 8 • 7, 
, 324D = (2 • D – 4)3, 33D5 = (D3 + 3) • 5, 345C = C53 • 4, 34BA = BA • 43, 
, 3839 = (3 + 8)3 • 9, 3CAD = A3 • D – C, 3D4A = DA • 43, 3D66 = (D3 – 6) • 6, 3D96 = D3 • 6 + 9, 3DE6 = D3 + E • 6, 3EBA = (B3 + E) • A, 450B = B4 – 5 – 0, 4511 = (11 – 5)4, 452B = B4 + 52, 
, 4639 = 49 • 63, 491C = 9 • C4 – 1, 4961 = (4 + 1)6 – 9, 4965 = (9 – 4)6 – 5, 496A = (A + 4 – 9)6, 496E = 4 + (–9 + E)6, 4CD2 = 2C • 4 + D, 
, 58DA = 85D • A, 6224 = (6 • 2)4 – 2, 6226 = (6 • 2)6 – 2, 622C = C2 + 2 + 6, 624C = C4 + 62, 7DCB = C7 • D • B, 86AC = A86 • C, 
, 8DA5 = D58 • A, AC21 = (C1 + A)2, AC1B = CB2 + A, B23C = 3B2 • C, BDEC = EDB • C, C20A = 2C + 0 • 10, C42E = (C4 – E) • 2, C452 = C4 • 2 + 5, CE2D = DE2 + C, D0E2 = E02 – D, DC56 = (D – C + 5)6, E326 = (E3 + 6)2, E329 = E92 + 3
, 1803 = 801 • 3, 1830 = 81 • 30, 192C = 219 • C, 19DE = 1D9 • E, 1E2A = 21 • EA, 2373 = 372 • 3, 27D0 = D0 • 72, 2BA8 = (2A – 8) • B, 2F78 = F8 • 72, 32FA = 3A • F2, 3342 = (3 • 3)4 • 2, 3A27 = 7A2 + 3, 3F48 = 438 • F, 41A7 = 74 + 1A, 41EB = 4B • F1, 4628 = 862 + 4, 467E = (64 – 7) • E, 46E0 = 64 • E + 0, 46E1 = 64 • E + 1, 46E2 = 64 • E + 2, 46E3 = 64 • E + 3, 46E4 = 64 • E + 4, 46E5 = 64 • E + 5, 46E6 = 64 • E + 6, 46E7 = 64 • E + 7, 46E8 = 64 • E + 8, 46E9 = 64 • E + 9, 46EA = 64 • E + A, 46EB = 64 • E + B, 46EC = 64 • E + C, 46ED = 64 • E + D, 46EE = 64 • E + E, 46EF = 64 • E + F, 4D39 = –4 + D3 • 9, 4D3D = D3 • (D – 4), 52B7 = (5 • B)2 • 7, 55C7 = 55 + C • 7, 57C0 = 75 • C0, 59DC = D5 • C • 9, 5EC6 = 6C5 • E, 5F7C = 7F5 • C, 618F = 681 • F, 672B = 76 – 2 • B, 76BA = B6 • A7, 7DFA = D7 • A • F, 85FC = 8C • F5, DF2E = EF2 + D, E0F2 = F02 – E, E695 = –E – 6 + 95