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Primes p such that (p^2 + p + 1)/7 is prime.
1

%I #18 May 05 2016 04:27:02

%S 11,23,53,179,233,317,389,401,443,599,641,683,977,1019,1061,1187,1229,

%T 1409,1481,1523,1619,1787,1997,2069,2111,2657,2963,3299,3329,3371,

%U 3413,3593,3677,3719,4139,4421,4463,5009,5147,5189,5231,5303,5387,5693

%N Primes p such that (p^2 + p + 1)/7 is prime.

%C Primes in A002641.

%H Seiichi Manyama, <a href="/A272628/b272628.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 11 because (11^2+11+1)/7 = 19 is a prime.

%t Select[Prime[Range[5000]], PrimeQ[(#^2 + # + 1) / 7] &]

%o (PARI) lista(nn) = {forprime(p=2, nn, if ((denominator(q=(p^2 + p + 1)/7) == 1) && isprime(q), print1(p, ", ")););} \\ _Michel Marcus_, May 05 2016

%Y Cf. A002641.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, May 04 2016