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A133287
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Decimal numbers that when converted to hexadecimal produce a number that uses the same digits as the original number.
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1
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 53, 371, 913, 4100, 5141, 5412, 6182, 8200, 9241, 75120, 75121, 75122, 75123, 75124, 75125, 75126, 75127, 75128, 75129, 75621, 86150, 91465, 98711, 99481
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OFFSET
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1,3
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COMMENTS
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There are 24 numbers in all, not including single-digit numbers, that produce their anagram when converted in hexadecimal.
The decimal and hexadecimal representations must have the same digits in the same proportions. For this reason a number like 1040 is not in the sequence: it is 410 in hexadecimal and thus lacks the second zero. - Alonso del Arte, Mar 04 2013
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LINKS
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EXAMPLE
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53 = 35_16; 371 = 173_16; 913 = 391_16; 4100 = 1004_16.
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MATHEMATICA
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Select[Range[0, 10000], Sort[IntegerDigits[#, 10]] == Sort[IntegerDigits[#, 16]] &] (* Alonso del Arte, Mar 04 2013 *)
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PROG
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(C++) #include <stdio.h> #include <string.h> char area1[8], area2[8]; long unsigned l; char c1[16], c2[16]; void main() { unsigned register a, b; for (l = 10; l < 100000lu; ++l) { sprintf(area1, "%lu", l); sprintf(area2, "%lx", l); if (strlen(area1) != strlen(area2)) continue; memset(c1, 0, 16); memset(c2, 0, 16); for (a = 0; b = area1[a]; ++a) ++c1[b&0xf]; for (a = 0; b = area2[a]; ++a) { if (b >= 'A') b -= 7; ++c2[b&0xf]; } for (a = 0;; ) { if (c1[a] != c2[a]) break; if (++a >= 16) printf("%s=%s(hex) ", area1, area2); } } }
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CROSSREFS
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KEYWORD
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base,easy,fini,nonn,full
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AUTHOR
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STATUS
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approved
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