A252484 Numbers m such that m^k is zeroless for k=1,...,4.

1, 2, 3, 4, 5, 6, 9, 11, 13, 14, 17, 21, 23, 24, 26, 27, 28, 31, 36, 39, 41, 46, 56, 58, 61, 62, 66, 68, 72, 76, 82, 83, 88, 91, 92, 96, 121, 122, 129, 137, 146, 154, 161, 162, 166, 167, 168, 183, 186, 188, 189, 211, 231, 233, 244, 256, 262, 264, 268, 277, 278, 289, 296, 337, 373, 374, 376, 382, 383

Offset: 1

Author

M. F. Hasler, Jan 07 2015

Keywords

• nonn
• base

Comments

See A253110 for the primes in this sequence. See A253644 for the subsequence including k=5.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A052382, A253643 (k <= 3), A253644 (k <= 5), A253645 (primes, k <= 5), A253647 (k <= 6), A253646 (primes, k <= 6), A124648 (k <= 7), A124649 (k <= 8).

Cf. A104264.

Programs

Maple

filter:= proc(n)
local j;
for j from 0 to 4 do
  if has(convert(n^j,base,10),0) then return false fi
od:
true
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 15 2015

Mathematica

Select[Range[400],Union[DigitCount[#^Range[4],10,0]]=={0}&] (* Harvey P. Dale, Aug 01 2020 *)

PARI

is_A252484(n,K=4)=!forstep(k=K,1,-1,vecmin(digits(n^k))||return)