A235635 - OEIS

A235635

Primes whose base-5 representation is also the base-7 representation of a prime.

2, 3, 5, 13, 17, 23, 29, 41, 43, 47, 53, 59, 61, 71, 79, 83, 101, 103, 137, 157, 163, 181, 191, 223, 227, 239, 281, 347, 379, 383, 419, 443, 463, 479, 547, 563, 571, 593, 641, 691, 701, 743, 757, 811, 839, 863, 877, 967, 997, 1049, 1051, 1087, 1097, 1109, 1151, 1171, 1217, 1249, 1259, 1283

(list; graph; refs; listen; history; text; internal format)

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

17 = 32_5 and 32_7 = 23 are both prime, so 17 is a term.

MATHEMATICA

Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 5], 7] &] (* Giovanni Resta, Sep 12 2019 *)

PROG

(PARI) is(p, b=7, c=5)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

CROSSREFS

Cf. A235627, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A249016 A241123 A038983 * A253645 A214802 A262840

Adjacent sequences: A235632 A235633 A235634 * A235636 A235637 A235638

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jan 13 2014

STATUS

approved