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Search: id:A112258
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| A112258 |
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Numbers n not divisible by 10 such that the decimal representation of n^26 does not use every nonzero digit. |
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+0
1
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| 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 17, 23, 29, 39, 61, 81, 95, 119, 164, 242, 5193, 9004, 23432, 246968, 8876708, 32886598
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Multiples of 10 are excluded because (10*n)^k uses the same nonzero digits as n^k. - No more terms < 10^8. Is the sequence finite?
Similar sequences can be defined for other positive integer exponents. 26 is the smallest exponent such that the corresponding sequence has less than 30 terms < 10^8.
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LINKS
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Eric Weisstein's World of Mathematics, Pandigital.
Patrick De Geest, The Nine Digits Page..
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EXAMPLE
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5^26 = 1490116119384765625 uses every digit, so 5 is not in the sequence.
6^26 = 170581728179578208256 does not use digits 3 and 4, so 6 is a term.
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PROGRAM
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(PARI) {e=26; for(n=1, 35000000, if(n%10>0, v=vector(9); c=0; k=n^e; while(c<9&&k>0, g=divrem(k, 10); k=g[1]; if(g[2]>0&&v[g[2]]==0, v[g[2]]=1; c++)); if(c<9, print1(n, ", "))))}
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CROSSREFS
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Cf. A089081 (26th powers).
Adjacent sequences: A112255 A112256 A112257 this_sequence A112259 A112260 A112261
Sequence in context: A030706 A101883 A035246 this_sequence A032893 A032852 A031990
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KEYWORD
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nonn,base,more
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 30 2005
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