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

%I #14 Sep 08 2022 08:45:40

%S 3,7,11,23,31,43,59,67,71,107,127,139,151,239,251,283,359,367,379,479,

%T 491,587,599,631,647,659,787,811,863,919,983,991,1031,1063,1171,1303,

%U 1319,1423,1427,1483,1523,1579,1583,1607,1627,1723,1831,1847,1907,1931,1999

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

%C The associated primes of the quadratic form are in A164580.

%H Vincenzo Librandi, <a href="/A154427/b154427.txt">Table of n, a(n) for n = 1..1000</a>

%e For p=7, p^2+(p+1)/2=53 is prime, which adds p=7 to the sequence.

%t Select[Prime[Range[500]],PrimeQ[#^2+(#+1)/2]&]

%t [_Harvey P. Dale_, Dec 19 2010]

%o (Magma) [p: p in PrimesInInterval(3,2000) | IsPrime(p^2+(p+1) div 2)]; // _Vincenzo Librandi_, Oct 12 2012

%Y Cf. A164580.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Aug 17 2009

%E Edited and extended by _R. J. Mathar_, Aug 26 2009