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A262833 (7,2)-primes (defined in Comments).

%I A262833 #6 Nov 09 2015 16:23:00
%S A262833 2,3,5,7,17,31,43,47,61,71,73,89,101,103,113,127,157,173,197,199,229,
%T A262833 239,241,269,271,281,311,337,353,367,379,383,397,409,439,449,463,479,
%U A262833 509,521,577,607,617,631,647,661,673,677,719,743,761,827,857,887,911
%N A262833 (7,2)-primes (defined in Comments).
%C A262833 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 A262833 Clark Kimberling, <a href="/A262833/b262833.txt">Table of n, a(n) for n = 1..10000</a>
%t A262833 {b1, b2} = {2, 7};
%t A262833 u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235477 *)
%t A262833 v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262833 *)
%t A262833 w = Intersection[u, v]; (* A262834 *)
%t A262833 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A262833 Cf. A000040, A262729, A262832, A262834.
%K A262833 nonn,easy,base
%O A262833 1,1
%A A262833 _Clark Kimberling_, Nov 01 2015