A262728 - OEIS

%I #11 Nov 07 2015 06:31:44

%S 2,173,181,233,443,877,967,1373,1831,4001,4231,4663,8191,8753,9043,

%T 10333,10631,13537,14591,16931,18211,25411,32707,32843,33637,37573,

%U 54773,56167,63853,64513,78101,84131,100207,102667,106087,112571,113153,133087,149531

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

%C 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).

%H Clark Kimberling, <a href="/A262728/b262728.txt">Table of n, a(n) for n = 1..1000</a>

%e Consider the number a(2) = 173:

%e in base 2, a(2) = 10101101, which is the prime 172;

%e in base 3, 10101101 is the prime 2467;

%e in base 5, 10101101 is the prime 81401;

%e in base 7, 10101101 is the prime 840743

%t {b1, b2, b3, b4} = {2, 3, 5, 7}; z = 15000;

%t u = Select[Prime[Range[z]],

%t PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &&

%t PrimeQ[FromDigits[IntegerDigits[#, b1], b3]] &&

%t PrimeQ[FromDigits[IntegerDigits[#, b1], b4]] &]

%t (* _Peter J. C. Moses_, Sep 27 2015 *)

%Y Cf. A000040, A262729.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 02 2015