A262728 (2,3,5,7)-primes (see comments for precise definition).

2, 173, 181, 233, 443, 877, 967, 1373, 1831, 4001, 4231, 4663, 8191, 8753, 9043, 10333, 10631, 13537, 14591, 16931, 18211, 25411, 32707, 32843, 33637, 37573, 54773, 56167, 63853, 64513, 78101, 84131, 100207, 102667, 106087, 112571, 113153, 133087, 149531

Offset: 1

Author

Clark Kimberling, Oct 02 2015

Keywords

• nonn
• easy
• base

Comments

Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k).

Examples

			Consider the number a(2) = 173:
in base 2, a(2) = 10101101, which is the prime 172;
in base 3, 10101101 is the prime 2467;
in base 5, 10101101 is the prime 81401;
in base 7, 10101101 is the prime 840743
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A262729.

Programs

Mathematica

{b1, b2, b3, b4} = {2, 3, 5, 7}; z = 15000;
u = Select[Prime[Range[z]],
PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&
PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&
PrimeQ[FromDigits[IntegerDigits[#, b1], b4]] &]
(* Peter J. C. Moses, Sep 27 2015 *)