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%I A231477 #15 Jan 16 2022 23:09:20
%S A231477 2,3,23,41,47,53,61,67,71,89,113,127,131,137,191,193,223,251,269,283,
%T A231477 293,311,353,397,409,421,443,463,491,503,509,541,569,601,613,701,773,
%U A231477 787,983,1013,1031,1091,1117,1213,1223,1429,1499,1543,1549,1579,1619,1621,1697,1699,1733,1873,1933,1949,1951,1973
%N A231477 Primes whose base-3 representation is also the base-7 representation of a prime.
%C A231477 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 A231477 Giovanni Resta, <a href="/A231477/b231477.txt">Table of n, a(n) for n = 1..10000</a>
%H A231477 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 A231477 23 = 212_3 and 212_7 = 107 are both prime, so 23 is a term.
%t A231477 Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 3], 7] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o A231477 (PARI) is(p,b=7,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y A231477 Cf. A235470, A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.
%K A231477 nonn,base
%O A231477 1,1
%A A231477 _M. F. Hasler_, Jan 12 2014

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