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A262834 {2,7}-primes (defined in Comments).

%I A262834 #8 Nov 09 2015 16:23:08
%S A262834 2,31,47,103,173,199,229,367,409,463,743,827,911,967,1123,1163,1321,
%T A262834 1447,1583,1657,1669,2161,2647,2677,2861,3361,3673,3851,4079,4231,
%U A262834 4271,4513,4663,5003,5381,5923,6329,6569,7043,7103,7393,7561,8263,8753,9649,10337
%N A262834 {2,7}-primes (defined in Comments).
%C A262834 Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p an S-prime if the digits of p in base b(i) spell a prime in each of the bases b(j) in S, for i = 1..k. Equivalently, p is an S-prime if p is a strong-V prime (defined at A262729) for every permutation of the vector V = (b(1), b(2), ..., b(k)).
%H A262834 Clark Kimberling, <a href="/A262834/b262834.txt">Table of n, a(n) for n = 1..1000</a>
%t A262834 {b1, b2} = {2, 7};
%t A262834 u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235477 *)
%t A262834 v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262833 *)
%t A262834 w = Intersection[u, v]; (* A262834 *)
%t A262834 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A262834 Cf. A000040, A262729, A235266, A262833.
%K A262834 nonn,easy,base
%O A262834 1,1
%A A262834 _Clark Kimberling_, Nov 05 2015