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%I #18 Sep 07 2018 17:41:56
%S 2,3,5,13,17,23,31,137,233,337,383,719,971,1291,1663,1777,3623,6113,
%T 12589,15733,15791,17729,22637,44623,48989,61379,65777,72379,82129,
%U 91331,99559,132859,133733,163633,226129,239539,346391,352133,394223,415379,428531,485113,518233,546523
%N Primes p such that p^k is zeroless for k=0,...,5.
%C These are the primes in A253644. This is a subsequence of A253110 (k<=4) and contains A253646 (k <= 6) as a subsequence.
%C Motivated by A253646, i.e., the observation that many small primes satisfy this condition for k <= 5 (52 terms below 10^6) but only very few satisfy it for k <= 6 (only 2 terms between 20 and 2*10^9).
%H Giovanni Resta, <a href="/A253645/b253645.txt">Table of n, a(n) for n = 1..5300</a> (first 1200 terms from Zak Seidov)
%t Select[Prime[Range[46000]],Count[Flatten[IntegerDigits/@(#^Range[5])],0] == 0&] (* _Harvey P. Dale_, Jan 13 2015 *)
%o (PARI) forprime(p=0,,forstep(k=5,1,-1,vecmin(digits(p^k))||next(2));print1(p","))
%Y Cf. A253110, A253644, A253646.
%K nonn,base
%O 1,1
%A _Zak Seidov_ and _M. F. Hasler_, Jan 07 2015
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