A231478 Primes whose base-3 representation is also the base-8 representation of a prime.

2, 7, 13, 31, 37, 43, 67, 73, 97, 193, 283, 307, 379, 457, 487, 499, 577, 619, 643, 727, 733, 757, 829, 1297, 1321, 1429, 1447, 1609, 1669, 1693, 2011, 2083, 2137, 2251, 2269, 2347, 2539, 2803, 2857, 2953, 2971

Offset: 1

Author

M. F. Hasler, Jan 12 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

			13 = 111_3 and 111_8 = 73 are both prime, so 13 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. A235471, A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 3], 8] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=8,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.