A261967 {2,3,5}-primes. (See comments.)

2, 151, 3061, 9517861, 11903341, 15344551, 15460771, 19975771, 37935091, 42234271, 52312411, 199938421, 228523501, 237049321, 270798991, 315266641, 315522931, 327445201, 354600601, 423223741, 466801171, 498309631, 499063711, 547916791, 585381361, 621504721

Offset

1,1

Comments

Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for i = 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 and j = 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)). Note that strong (2,3,5)-primes (A262727) form a proper subset of {2,3,5}-primes. It may be of interest to consider the sets of {2,3,5,7}-primes, {2,3,5,7,11}-primes, etc. Is every such set infinite?

Links

Table of n, a(n) for n=1..26.

Mathematica

{b1, b2, b3} = {2, 3, 5}; z = 10000000;
Select[Prime[Range[z]],
PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&
PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&
PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &&
PrimeQ[FromDigits[IntegerDigits[#, b2], b3]] &&
PrimeQ[FromDigits[IntegerDigits[#, b3], b1]] &&
PrimeQ[FromDigits[IntegerDigits[#, b3], b2]] &]
(* Peter J. C. Moses, Sep 27 2015 *)

Crossrefs

Cf. A000040, A235266, A262727, A262841, A262728, A262729.

Sequence in context: A329712 A128350 A046473 * A024245 A113576 A102458

Adjacent sequences: A261964 A261965 A261966 * A261968 A261969 A261970

Keyword

nonn,easy,base

Author

Clark Kimberling, Nov 09 2015

Status

approved