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%I #20 Jan 17 2022 00:32:25
%S 2,3,5,11,19,23,29,37,47,67,71,89,103,107,113,127,137,163,179,239,257,
%T 313,337,347,389,401,431,457,463,499,523,547,569,571,617,709,719,739,
%U 743,751,757,761,821,823,859,883,887,971,1019,1069,1093,1129,1153,1213,1297,1307,1327,1367,1373,1381
%N Primes whose base-7 representation is also 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.
%H Giovanni Resta, <a href="/A231479/b231479.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 = 14_7 and 14_9 = 13 are both prime, so 11 is a term.
%t Select[Prime@ Range@ 250, PrimeQ@ FromDigits[IntegerDigits[#, 7], 9] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o (PARI) is(p,b=9,c=7)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y Cf. A235621, A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Jan 12 2014
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