A235631 Primes whose base-6 representation is also the base-8 representation of a prime.

2, 3, 5, 11, 13, 23, 29, 31, 43, 61, 71, 79, 89, 107, 109, 113, 137, 139, 163, 173, 193, 223, 239, 251, 271, 281, 283, 313, 317, 347, 383, 431, 439, 461, 467, 491, 499, 541, 557, 593, 607, 641, 659, 661, 691, 701, 743, 761, 853, 863, 881, 919, 971, 997, 1013, 1031, 1051, 1061, 1063

Offset: 1

Author

M. F. Hasler, Jan 13 2014

Keywords

• nonn
• base

Comments

This sequence is part of a two-dimensional array of sequences, given in the LINK, 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

			11 = 15_6 and 15_8 = 13 are both prime, so 11 is a term.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235638, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 6], 8] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=8,c=6)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.