%I #17 Jan 16 2022 23:21:16

%S 2,3,5,13,17,23,29,41,43,47,53,59,61,71,79,83,101,103,137,157,163,181,

%T 191,223,227,239,281,347,379,383,419,443,463,479,547,563,571,593,641,

%U 691,701,743,757,811,839,863,877,967,997,1049,1051,1087,1097,1109,1151,1171,1217,1249,1259,1283

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

%C 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.

%H Giovanni Resta, <a href="/A235635/b235635.txt">Table of n, a(n) for n = 1..10000</a>

%H M. F. Hasler, <a href="https://docs.google.com/document/d/10IM7fcAbB2tqRGuwfGvuEGUzD_IXbgXPDK0tfxN4M3o/pub">Primes whose base c expansion is also the base b expansion of a prime</a>

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

%t Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 5], 7] &] (* _Giovanni Resta_, Sep 12 2019 *)

%o (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.

%Y 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.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 13 2014