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A233540 Primes p such that p+2, p+8, and p+12 are all prime.

%I A233540 #27 Aug 20 2019 08:27:04
%S A233540 5,11,29,59,71,101,269,431,1289,1481,2129,2339,2381,2789,4721,5519,
%T A233540 5639,5849,6569,6959,8999,10091,13679,14549,16061,16649,16691,18119,
%U A233540 19379,19421,19751,21011,21491,22271,25931,27689,27791,28619,31181,32369,32561,32831
%N A233540 Primes p such that p+2, p+8, and p+12 are all prime.
%C A233540 The primes produced (p, p+2, p+8, p+12) are not always consecutive primes.
%H A233540 Michael B. Porter, <a href="/A233540/b233540.txt">Table of n, a(n) for n = 1..2300</a>
%F A233540 A046141 INTERSECT A046134. - _R. J. Mathar_, Aug 20 2019
%e A233540 29 is in the sequence because 29, 29 + 2 = 31, 29 + 8 = 37, and 29 + 12 = 41 are all prime.
%p A233540 KD := proc() local a,b,c,p; p:=ithprime(n);a:=p+2;b:=p+8;c:=p+12;if isprime(a)and isprime(b) and isprime(c) then RETURN (p); fi; end: seq(KD(), n=1..10000);
%p A233540 # _K. D. Bajpai_, Dec 27 2013
%t A233540 Select[Prime[Range[4000]],AllTrue[#+{2,8,12},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 04 2016 *)
%o A233540 (PARI) is_a233540(p) = isprime(p) && isprime(p+2) && isprime(p+8) && isprime(p+12) \\ _Michael B. Porter_, Dec 27 2013
%Y A233540 Cf. A007530 (prime quadruples).
%Y A233540 Cf. A078848 (same prime differences, but with consecutive primes).
%K A233540 nonn
%O A233540 1,1
%A A233540 _K. D. Bajpai_, Dec 12 2013