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%I #15 Nov 02 2023 10:39:16
%S 2,3,5,19,61,89,127,131,173,211,229,257,281,383,397,421,463,467,523,
%T 547,593,617,719,757,761,859,883,911,953,967,971,1069,1097,1153,1163,
%U 1181,1303,1307,1429,1433,1471,1489,1531,1583,1597,1723,1741,1867,1877,1951,1979,1993,2437
%N Primes whose base-7 representation also is the base-6 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="/A235637/b235637.txt">Table of n, a(n) for n = 1..14278</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 E.g., 19 = 25_7 and 25_6 = 17 are both prime.
%o (PARI) is(p,b=6,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,7,6)&&print1(vector(#d=digits(p,6),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,6,7)
%Y Cf. A235636, 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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