A253645 Primes p such that p^k is zeroless for k=0,...,5.

2, 3, 5, 13, 17, 23, 31, 137, 233, 337, 383, 719, 971, 1291, 1663, 1777, 3623, 6113, 12589, 15733, 15791, 17729, 22637, 44623, 48989, 61379, 65777, 72379, 82129, 91331, 99559, 132859, 133733, 163633, 226129, 239539, 346391, 352133, 394223, 415379, 428531, 485113, 518233, 546523

Offset: 1

Author

Zak Seidov and M. F. Hasler, Jan 07 2015

Keywords

• nonn
• base

Comments

These are the primes in A253644. This is a subsequence of A253110 (k<=4) and contains A253646 (k <= 6) as a subsequence.

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).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..5300 (first 1200 terms from Zak Seidov)

Crossrefs

Cf. A253110, A253644, A253646.

Programs

Mathematica

Select[Prime[Range[46000]],Count[Flatten[IntegerDigits/@(#^Range[5])],0] == 0&] (* Harvey P. Dale, Jan 13 2015 *)

PARI

forprime(p=0,,forstep(k=5,1,-1,vecmin(digits(p^k))||next(2));print1(p","))