A261967 - OEIS

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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

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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 *)