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A199634
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Number of pandigital numbers raised to the n-th power is a number in which each digit appears n times.
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0
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3265920, 534, 74, 13, 8, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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Note that a(1) is the number of pandigital numbers, 10! - 9! = 9*9!. For n > 1, it is the number of numbers in A199630, A199631, A114260, A199632, and A199633.
The Mathematica code takes many hours to run. The program stops after doing power 186 because the largest pandigital number 9876543210 raised to any greater power does not produce enough digits.
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LINKS
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Table of n, a(n) for n=1..83.
Patrick De Geest, The nine digits (page 4) with some ten digit (pandigital) exceptions
Author?, All terms
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MATHEMATICA
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t = {}; perm = Select[Permutations[Range[0, 9]], #[[1]] > 0 &]; len = Length[perm]; Print[{1, len}]; AppendTo[t, len]; pwr = 1; i = 1; While[pwr++; i < len, While[IntegerLength[FromDigits[perm[[i]]]^pwr] < 10*pwr, i++]; cnt = 0; Do[If[Union[DigitCount[FromDigits[perm[[j]]]^pwr]] == {pwr}, cnt++], {j, i, len}]; Print[{pwr, cnt}]; AppendTo[t, cnt]]
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CROSSREFS
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Cf. A050278 (pandigital numbers).
Sequence in context: A203731 A138360 A206083 * A203987 A217110 A217111
Adjacent sequences: A199631 A199632 A199633 * A199635 A199636 A199637
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KEYWORD
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nonn,base
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AUTHOR
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T. D. Noe, Nov 09 2011
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STATUS
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approved
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