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%I #15 Jan 16 2022 23:22:33
%S 2,3,5,19,53,89,109,131,257,293,307,347,349,433,523,557,683,739,811,
%T 853,881,907,937,941,1061,1097,1117,1201,1427,1621,1693,1733,1747,
%U 1861,1873,1889,1907,2141,2267,2341,2467,2677,2699,2803,2861,2917,2953,3163,3253,3307,3433
%N Primes whose base-8 representation also is the base-7 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 Harvey P. Dale, <a href="/A235622/b235622.txt">Table of n, a(n) for n = 1..1000</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 = 23_8 and 23_7 = 17 are both prime.
%t pb87Q[n_]:=Module[{idn8=IntegerDigits[n,8]},Max[idn8]<7&&PrimeQ[ FromDigits[ idn8,7]]]; Select[Prime[Range[500]],pb87Q] (* _Harvey P. Dale_, Dec 13 2016 *)
%o (PARI) is(p,b=7,c=8)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o (PARI) forprime(p=1,3e3,is(p,8,7)&&print1(vector(#d=digits(p,7),i,8^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,7,8)
%Y Cf. A235630, 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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