A278697 Primes p such that every suffix of the base-5 representation of p is a prime.

2, 3, 7, 13, 17, 23, 53, 67, 73, 103, 107, 113, 127, 257, 263, 317, 353, 503, 523, 607, 613, 1303, 1567, 1753, 1877, 2503, 3023, 6257, 6263, 6317, 6323, 6353, 6857, 6863, 7817, 8753, 9377, 12503, 12517, 12553, 12613, 12757, 12763, 12853, 13003, 31253, 31267, 31357, 31513, 31567

Offset: 1

Author

Randy L. Ekl, Nov 26 2016

Keywords

• nonn
• base

Examples

			17=32_5 is in the sequence since it and its base-5 suffix (2_5=2) are primes.
113=423_5 is in the sequence since it and each of its base-5 suffixes (23_5=13 and 3_5=3) are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033664 is in base 10.

Programs

Maple

F[1]:= [2,3]:
for m from 2 while nops(F[m-1]) < 100 do
  F[m]:= [op(F[m-1]),op(select(isprime, [seq(seq(i*5^
(m-1)+x,x=F[m-1]),i=1..4)]))]
od:
F[m-1]; # Robert Israel, Jan 22 2020

PARI

isok(n) = {if (isprime(n), pp = 5^logint(n, 5); while (isprime(n % pp) && (pp != 1), pp = pp/5); pp == 1;);} \\ Michel Marcus, Nov 26 2016