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A262829 (3,2)-primes (defined in Comments).

%I A262829 #7 Oct 26 2015 22:25:00
%S A262829 2,3,7,13,31,37,43,67,79,151,157,181,193,223,241,271,283,307,331,349,
%T A262829 373,397,409,421,433,463,499,571,613,619,631,643,661,673,691,733,757,
%U A262829 769,787,829,853,877,937,997,1009,1093,1123,1129,1153,1201,1213,1231
%N A262829 (3,2)-primes (defined in Comments).
%C A262829 Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k).
%H A262829 Clark Kimberling, <a href="/A262829/b262829.txt">Table of n, a(n) for n = 1..10000</a>
%t A262829 {b1, b2} = {2, 3};
%t A262829 u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235266 *)
%t A262829 v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262829 *)
%t A262829 w = Intersection[u, v]; (* A262830 *)
%t A262829 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A262829 Cf. A000040, A235266, A262730.
%K A262829 nonn,easy,base
%O A262829 1,1
%A A262829 _Clark Kimberling_, Oct 24 2015