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%I #13 Nov 01 2023 23:20:56
%S 11,13,19,41,79,109,137,151,167,191,193,199,227,239,271,307,313,421,
%T 431,433,457,487,491,521,563,613,617,659,677,709,727,757,929,947,1009,
%U 1033,1051,1249,1483,1693,1697,1709,1721,1831,1951,1979,1987,1993
%N Primes whose base-2 representation also is the base-9 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.
%C For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
%C A subsequence of A027697, A050150, A062090 and A176620.
%H Robert Price, <a href="/A235479/b235479.txt">Table of n, a(n) for n = 1..1958</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 11 = 1011_2 and 1011_9 = 6571 are both prime, so 11 is a term.
%o (PARI) is(p,b=9)=isprime(vector(#d=binary(p),i,b^(#d-i))*d~)&&isprime(p)
%Y Cf. A235466 ⊂ A077723, A235266, A152079, A235475 - A235478, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Jan 12 2014
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