A253647 Numbers n such that n^k is zeroless for k=0,...,6.

1, 2, 3, 5, 6, 14, 17, 68, 76, 96, 188, 483, 518, 582, 736, 786, 1331, 1414, 3944, 4214, 6112, 6676, 8256, 8583, 8686, 9738, 15314, 15483, 33736, 44712, 48989, 61562, 71689, 78512, 93711, 121568, 187791, 239477, 292958, 315426, 545866, 763142, 792612, 1391739

Offset: 1

Author

M. F. Hasler, Jan 07 2015

Keywords

• nonn
• base

Comments

Contains A124648 as a subsequence. Primes in this sequence are listed in A253646.

There are 55 terms below 10^7. Conjectured to be finite.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..191 (terms < 3.3*10^16)

Crossrefs

Cf. A052382, A104264, A124648, A124649, A253645, A253646.

Programs

Mathematica

Select[Range[14*10^5],Count[Flatten[IntegerDigits/@(#^Range[ 0,6])],0] == 0&] (* Harvey P. Dale, Apr 29 2018 *)

PARI

is_A253647(n,K=6)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)