A262840 {5,7}-primes (defined in Comments).

2, 3, 5, 13, 17, 23, 41, 43, 53, 71, 79, 101, 137, 157, 181, 191, 239, 281, 379, 463, 743, 839, 863, 967, 1151, 1171, 1303, 1367, 1663, 1721, 2083, 2251, 2297, 2351, 2621, 2659, 2957, 2999, 3257, 3343, 3373, 3511, 3607, 3767, 3863, 3877, 3907, 4217, 4447

Offset

1,1

Comments

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)).

Links

Clark Kimberling, Table of n, a(n) for n = 1..5000

Mathematica

{b1, b2} = {5, 7};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &];  (* A235635 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262839 *)
w = Intersection[u, v]; (* A262840 *)
(* Peter J. C. Moses, Sep 27 2015 *)

Crossrefs

Cf. A000040, A235635, A262839, A262829.

Sequence in context: A235635 A253645 A214802 * A215318 A186945 A193761

Adjacent sequences: A262837 A262838 A262839 * A262841 A262842 A262843

Keyword

nonn,easy,base

Author

Clark Kimberling, Nov 09 2015

Status

approved