A262834 - OEIS

%I #8 Nov 09 2015 16:23:08

%S 2,31,47,103,173,199,229,367,409,463,743,827,911,967,1123,1163,1321,

%T 1447,1583,1657,1669,2161,2647,2677,2861,3361,3673,3851,4079,4231,

%U 4271,4513,4663,5003,5381,5923,6329,6569,7043,7103,7393,7561,8263,8753,9649,10337

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

%C 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 Clark Kimberling, <a href="/A262834/b262834.txt">Table of n, a(n) for n = 1..1000</a>

%t {b1, b2} = {2, 7};

%t u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235477 *)

%t v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262833 *)

%t w = Intersection[u, v]; (* A262834 *)

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

%Y Cf. A000040, A262729, A235266, A262833.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Nov 05 2015