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A290817 Primes of at least one of the forms p^2 +- p +- 1, where p is prime.

%I A290817 #44 Sep 08 2022 08:46:19
%S A290817 3,5,7,11,13,19,29,31,41,43,109,131,157,181,271,307,379,811,929,991,
%T A290817 1721,1723,2161,2861,3539,3541,3659,4421,4423,4969,5113,6163,6971,
%U A290817 8009,8011,9311,10099,10301,10303,10711,16001,17029,17291,17293,19181,19183,22051,22349,22651
%N A290817 Primes of at least one of the forms p^2 +- p +- 1, where p is prime.
%C A290817 This sequence contains prime chains and prime trees using an appropriate mapping form p^2 +- p +- 1 in each step, such as the chain: 3 -> 5 -> 19 -> 379 -> 143263 -> 20524143907 and the tree: 41 -> {1721, 1723}.
%H A290817 Robert Israel, <a href="/A290817/b290817.txt">Table of n, a(n) for n = 1..10000</a>
%p A290817 select(isprime, [3,seq(op([p^2-p-1,p^2-p+1,p^2+p-1,p^2+p+1]),p=select(isprime,[seq(i,i=3..1000,2)]))]); # _Robert Israel_, Nov 27 2019
%t A290817 Select[Union[Flatten[{(#^2 + # + 1 ), (#^2 + # - 1 ), (#^2 - # + 1 ), (#^2 - # - 1 )}] &[Prime[Range[100]]]], (PrimeQ[#]) &]
%o A290817 (Magma) {p^2+(-1)^k*p+(-1)^s:p in PrimesUpTo(150), s,k in [1..2]|IsPrime(p^2+(-1)^k*p+(-1)^s)}; //  _Marius A. Burtea_, Nov 28 2019
%Y A290817 Cf. A000040.
%Y A290817 Union of A053183, A053185, A074268, A091568.
%K A290817 nonn
%O A290817 1,1
%A A290817 _Ralf Steiner_, Aug 11 2017