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Primes whose base-6 representation is also the base-8 representation of a prime.
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%I #17 Jan 16 2022 23:27:23

%S 2,3,5,11,13,23,29,31,43,61,71,79,89,107,109,113,137,139,163,173,193,

%T 223,239,251,271,281,283,313,317,347,383,431,439,461,467,491,499,541,

%U 557,593,607,641,659,661,691,701,743,761,853,863,881,919,971,997,1013,1031,1051,1061,1063

%N Primes whose base-6 representation is also the base-8 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.

%H Giovanni Resta, <a href="/A235631/b235631.txt">Table of n, a(n) for n = 1..10000</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 = 15_6 and 15_8 = 13 are both prime, so 11 is a term.

%t Select[Prime@Range@500, PrimeQ@FromDigits[IntegerDigits[#, 6], 8] &] (* _Giovanni Resta_, Sep 12 2019 *)

%o (PARI) is(p,b=8,c=6)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

%Y Cf. A235638, 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