A235628 Primes whose base-8 representation also is the base-5 representation of a prime.

2, 3, 17, 19, 73, 89, 131, 163, 257, 521, 577, 739, 1097, 1171, 1283, 1601, 1747, 2081, 2083, 2137, 2267, 4177, 4289, 4363, 4643, 5273, 5387, 5651, 5779, 5849, 5851, 5923, 6211, 6299, 6337, 8353, 8713, 8803, 8929, 8969, 8971, 9377, 9419, 9473, 9491, 9811, 9883, 10009

Offset: 1

Author

M. F. Hasler, Jan 13 2014

Keywords

• nonn
• base

Comments

This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

Examples

			Both 17 = 23_8 and 23_5 = 13 are prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..3395
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235632, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

PARI

is(p,b=5,c=8)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,3e3,is(p,8,5)&&print1(vector(#d=digits(p,5),i,8^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,5,8)