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A262840
{5,7}-primes (defined in Comments).
2
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
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
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Nov 09 2015
STATUS
approved