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%I #22 Sep 08 2022 08:46:18
%S 3,5,17,197,1427,1667,2087,4157,4217,8387,8597,10037,11117,11717,
%T 15287,17417,20147,25847,29207,33347,33827,34847,35897,36527,47657,
%U 56237,57527,60257,63197,63587,69497,75167,77477,89657,93887,96797,99347,99527,100547
%N Primes p such that p+2, 3*p+2 and 3*p+8 are also primes.
%C If k = (a(n)+2)*(3*a(n)+2), then A000203(k) = A000203(k-A000005(k)), see Robert Israel's comment at A277273.
%H Iain Fox, <a href="/A278138/b278138.txt">Table of n, a(n) for n = 1..10000</a> (first 4356 terms from Robert Israel)
%p select(p -> isprime(3*p+8) and isprime(3*p+2) and isprime(p+2) and isprime(p), [3,seq(i,i=5..10^6,6)]); # _Robert Israel_, Nov 23 2016
%t Select[Prime[Range[10000]], Union[PrimeQ/@{# + 2, 3 # + 2, 3 # + 8}] == {True}&]
%o (MATLAB)
%o P = primes(10^6);
%o P1 = intersect(P, P-2);
%o P1 = intersect(P1, (P-2)/3);
%o P1 = intersect(P1, (P-8)/3) % _Robert Israel_, Nov 23 2016
%o (Magma) [p: p in PrimesUpTo(100000) | IsPrime(p+2) and IsPrime(3*p+2) and IsPrime(3*p+8)]; // _Vincenzo Librandi_, Nov 23 2016
%o (PARI) isok(p) = isprime(p) && isprime(p+2) && isprime(3*p+2) && isprime(3*p+8); \\ _Michel Marcus_, Dec 17 2017
%Y Cf. A000040, A277273.
%Y Subsequence of A001359.
%K nonn,easy
%O 1,1
%A _Ivan N. Ianakiev_, Nov 23 2016
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