A262834 {2,7}-primes (defined in Comments).

2, 31, 47, 103, 173, 199, 229, 367, 409, 463, 743, 827, 911, 967, 1123, 1163, 1321, 1447, 1583, 1657, 1669, 2161, 2647, 2677, 2861, 3361, 3673, 3851, 4079, 4231, 4271, 4513, 4663, 5003, 5381, 5923, 6329, 6569, 7043, 7103, 7393, 7561, 8263, 8753, 9649, 10337

Offset: 1

Author

Clark Kimberling, Nov 05 2015

Keywords

• nonn
• easy
• base

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..1000

Crossrefs

Cf. A000040, A262729, A235266, A262833.

Programs

Mathematica

{b1, b2} = {2, 7};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235477 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262833 *)
w = Intersection[u, v]; (* A262834 *)
(* Peter J. C. Moses, Sep 27 2015 *)