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%I #32 Jun 12 2018 15:03:21
%S 5,7,17,47,127,227,257,397,467,607,997,1447,1487,1697,1877,2647,3307,
%T 3547,3907,4217,4987,5407,6287,6947,7297,7537,7817,10067,10627,11047,
%U 11777,12227,12577,13147,14747,15137,15737,15877,17827,19727,19937,20707,21577,22027,22247,23017,24097,26017
%N Initial prime of 4 primes in arithmetic progression with difference 12.
%C Or, primes p such that p + 12, p + 24 and p + 36 are also primes.
%C Primes are not necessarily consecutive ones. A033447 is subsequence: a(92) = 111497 = A033447(1), a(144) = 258527 = A033447(2), etc.
%C The only case with p + 48 prime is p = 5, in all other cases p + 48 is divisible by 5.
%C All terms >5 are congruent to 7 (mod 10). - _Zak Seidov_, Jun 12 2018
%H Jens Kruse Andersen, <a href="/A248085/b248085.txt">Table of n, a(n) for n = 1..10000</a>
%p A248085:=n->`if`(isprime(n) and isprime(n+12) and isprime(n+24) and isprime(n+36), n, NULL): seq(A248085(n), n=1..10^5); # _Wesley Ivan Hurt_, Oct 01 2014
%t Select[Prime[Range[1000]], PrimeQ[# + 12] && PrimeQ[# + 24] && PrimeQ[# + 36] &] (* _Alonso del Arte_, Oct 01 2014 *)
%t Select[Prime[Range[3000]],AllTrue[#+{12,24,36},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 08 2016 *)
%o (PARI) forprime(p=5,10^5,isprime(p+12)&&isprime(p+24)&&isprime(p+36)&&print1(p","))
%Y Cf. A033447.
%K nonn
%O 1,1
%A _Zak Seidov_, Oct 01 2014
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