A231474 Primes whose base-3 representation is also the base-5 representation of a prime.

2, 3, 5, 7, 13, 17, 29, 31, 37, 41, 59, 67, 79, 97, 101, 109, 113, 137, 139, 149, 151, 173, 181, 193, 223, 229, 251, 269, 271, 293, 311, 331, 353, 367, 373, 379, 383, 389, 397, 401, 457, 467, 491, 503, 617, 631, 641, 647, 653, 673, 701, 773, 787, 797, 809, 829, 853, 857, 911, 929, 953, 977

Offset

1,1

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.

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

Example

7 = 21_3 and 21_5 = 11 are both prime, so 7 is a term.

Mathematica

Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 3], 5] &] (* Giovanni Resta, Sep 12 2019 *)

Prog

(PARI) is(p, b=5, c=3)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

Crossrefs

Cf. A235265, A235266, A235473, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.

Sequence in context: A233282 A001000 A094947 * A092621 A188809 A350443

Adjacent sequences: A231471 A231472 A231473 * A231475 A231476 A231477

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved