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%I #17 Nov 02 2023 14:18:24
%S 2,3,13,41,43,61,181,191,263,281,283,331,383,431,443,463,641,643,661,
%T 881,911,1063,1091,1291,1303,1531,1693,2083,2143,2203,2293,2341,3163,
%U 3181,3191,3253,3343,3593,3761,3931,4001,4093,4391,4691,4793,5011,5393,5413,5441,6301
%N Primes whose base-5 representation also is the base-4 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="/A235615/b235615.txt">Table of n, a(n) for n = 1..107268</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 13 = 23_5 and 23_4 = 11 are prime.
%o (PARI) is(p,b=4,c=5)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o (PARI) forprime(p=1,3e3,is(p,5,4)&&print1(vector(#d=digits(p,4),i,5^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,4,5)
%Y Cf. A235474, 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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