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%I #12 Nov 02 2023 10:39:20
%S 2,3,7,17,23,31,53,71,73,79,101,109,113,127,151,157,197,199,359,401,
%T 409,449,463,521,541,557,743,863,1033,1039,1103,1151,1193,1229,1451,
%U 1487,1499,1543,2423,2521,2549,2621,2753,2857,2909,2957,3089,3257,3313,3511,3529,3593
%N Primes whose base-7 representation also is the base-5 representation of a prime.
%C This sequence is part of the two-dimensional array of sequences 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 Robert Price, <a href="/A235627/b235627.txt">Table of n, a(n) for n = 1..13736</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 Both 17 = 23_7 and 23_5 = 13 are prime.
%o (PARI) is(p,b=5,c=7)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o (PARI) forprime(p=1,3e3,is(p,7,5)&&print1(vector(#d=digits(p,5),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,5,7)
%Y Cf. A235635, 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