cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A261967 #6 Nov 24 2015 01:41:43
%S A261967 2,151,3061,9517861,11903341,15344551,15460771,19975771,37935091,
%T A261967 42234271,52312411,199938421,228523501,237049321,270798991,315266641,
%U A261967 315522931,327445201,354600601,423223741,466801171,498309631,499063711,547916791,585381361,621504721
%N A261967 {2,3,5}-primes. (See comments.)
%C A261967 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?
%t A261967 {b1, b2, b3} = {2, 3, 5}; z = 10000000;
%t A261967 Select[Prime[Range[z]],
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &&
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b2], b3]] &&
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b3], b1]] &&
%t A261967 PrimeQ[FromDigits[IntegerDigits[#, b3], b2]] &]
%t A261967 (* _Peter J. C. Moses_, Sep 27 2015 *)
%Y A261967 Cf. A000040, A235266, A262727, A262841, A262728, A262729.
%K A261967 nonn,easy,base
%O A261967 1,1
%A A261967 _Clark Kimberling_, Nov 09 2015