A253644 Numbers n such that n^k is zeroless for k=0,...,5.

1, 2, 3, 5, 6, 13, 14, 17, 23, 24, 26, 31, 58, 62, 66, 68, 72, 76, 88, 96, 137, 168, 188, 233, 244, 262, 264, 296, 337, 376, 382, 383, 483, 488, 511, 514, 518, 519, 582, 628, 719, 736, 786, 816, 822, 928, 938, 971, 978, 1122, 1178, 1291, 1331, 1392, 1413, 1414, 1663, 1777

Offset: 1

Author

M. F. Hasler, Jan 07 2015

Keywords

• nonn
• base

Comments

A subsequence of A252484 (analog for k <= 4) which contains A253647 (analog including k = 6) as a subsequence. Primes in this sequence are listed in A253645.

Conjectured to be finite.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052382, A104264, A124648, A124649, A253645, A253646, A253647.

Programs

Maple

filter:= proc(x)
  local k;
  for k from 1 to 5 do
    if has(convert(x^k,base,10),0) then return false fi
  od:
  true
end proc:
select(filter, [$1..10000]); # Robert Israel, Jan 07 2015

Mathematica

Select[Range[2000],Count[Flatten[IntegerDigits/@(#^Range[5])],0]==0&] (* Harvey P. Dale, Jun 10 2017 *)

PARI

is_A253644(n,K=5)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)