A262840 - OEIS

%I #8 Nov 24 2015 01:42:31

%S 2,3,5,13,17,23,41,43,53,71,79,101,137,157,181,191,239,281,379,463,

%T 743,839,863,967,1151,1171,1303,1367,1663,1721,2083,2251,2297,2351,

%U 2621,2659,2957,2999,3257,3343,3373,3511,3607,3767,3863,3877,3907,4217,4447

%N {5,7}-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="/A262840/b262840.txt">Table of n, a(n) for n = 1..5000</a>

%t {b1, b2} = {5, 7};

%t u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A235635 *)

%t v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262839 *)

%t w = Intersection[u, v]; (* A262840 *)

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

%Y Cf. A000040, A235635, A262839, A262829.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Nov 09 2015