A199634 Number of pandigital numbers raised to the n-th power is a number in which each digit appears n times.

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

Offset: 1

Author

T. D. Noe, Nov 09 2011

Keywords

• nonn
• base

Comments

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, A365144, 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.

Links

• Patrick De Geest, The nine digits (page 4) with some ten digit (pandigital) exceptions
• Author?, All terms

Crossrefs

Cf. A050278 (pandigital numbers), A199630, A199631, A365144, A199632, A199633.

Programs

Mathematica

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]]