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%I #20 Jan 16 2022 23:27:36
%S 2,3,5,17,47,71,89,101,197,229,241,269,271,337,353,383,479,521,577,
%T 607,631,647,673,677,719,743,761,827,997,1097,1153,1181,1193,1279,
%U 1289,1303,1319,1447,1543,1601,1697,1811,1823,1907,1951,1993,2017,2131,2203,2243,2339,2357,2383,2549
%N Primes whose base-7 representation is also the base-8 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="/A235630/b235630.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 = 23_7 and 23_8 = 19 are both prime, so 17 is a term.
%t Select[Prime@Range@500, PrimeQ@ FromDigits[IntegerDigits[#, 7], 8] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o (PARI) is(p,b=8,c=7)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y Cf. A235622, 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
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