This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A235463 #21 Apr 14 2021 00:03:31
%S A235463 7,37,43,223,1297,1303,1549,7993,9109,46663,54469,55987,326593,
%T A235463 1679659,1681129,1727569,1734049,1967587,2006461,2007763,2014027,
%U A235463 2015287,10077919,10125649,10125691,10133467,10412107,10413397,11757349,11766421,11766427,11766637
%N A235463 Primes whose base-6 representation also is the base-2 representation of a prime.
%C A235463 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.
%C A235463 For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
%C A235463 When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=6, thus a subsequence of A077720.
%H A235463 Alois P. Heinz, <a href="/A235463/b235463.txt">Table of n, a(n) for n = 1..10000</a>
%H A235463 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 A235463 7 = 11_6 and 11_2 = 3 are both prime, so 7 is a term.
%e A235463 37 = 101_6 and 101_2 = 5 are both prime, so 37 is a term.
%t A235463 b62Q[n_]:=Module[{idn6=IntegerDigits[n,6]},Max[idn6]<2&&AllTrue[ {FromDigits[ idn6,6],FromDigits[idn6,2]},PrimeQ]]; Select[Prime[ Range[ 4,780000]],b62Q] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 29 2020 *)
%o A235463 (PARI) is(p,b=2,c=6)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o A235463 (PARI) forprime(p=1,1e3,is(p,6,2)&&print1(vector(#d=digits(p,2),i,6^(#d-i))*d~,",")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(.,2,6)
%Y A235463 Cf. A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.
%K A235463 nonn,base
%O A235463 1,1
%A A235463 _M. F. Hasler_, Jan 11 2014