A235625 Primes whose base-5 representation is also the base-6 representation of a prime.

2, 3, 11, 31, 71, 131, 191, 211, 241, 251, 271, 331, 421, 431, 461, 491, 541, 601, 631, 811, 821, 911, 971, 1031, 1051, 1061, 1171, 1181, 1201, 1231, 1291, 1321, 1361, 1451, 1511, 1531, 1571, 1601, 1721, 1801, 1811, 1831, 1861, 1931, 2081, 2111, 2131, 2141, 2311, 2341, 2381, 2411, 2521, 2531, 2711, 2741, 2801

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 = 21_5 and 21_6 = 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. A235626, 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[#, 5], 6] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=6,c=5)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.