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(5,3)-primes (defined in Comments).
2

%I #8 Nov 09 2015 16:23:15

%S 2,3,5,7,11,17,19,29,31,37,41,47,67,71,79,89,97,101,107,109,127,131,

%T 139,149,151,157,167,197,199,211,229,239,241,257,269,271,281,311,317,

%U 337,349,359,367,409,419,421,431,439,457,491,541,547,557,569,571,577

%N (5,3)-primes (defined in Comments).

%C 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 Clark Kimberling, <a href="/A262835/b262835.txt">Table of n, a(n) for n = 1..10000</a>

%t {b1, b2} = {3, 5};

%t u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A231474 *)

%t v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262835 *)

%t w = Intersection[u, v]; (* A262836 *)

%t (* _Peter J. C. Moses_, Sep 27 2015 *)

%Y Cf. A000040, A231474, A262836, A262829.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Nov 05 2015