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%I #21 Sep 22 2023 11:03:20
%S 3,13,7,2,2,2,3,2,2,2,3,2,2,3,2,3,2,3,2,2,3,7,2,2,3,2,2,3,7,2,3,7,11,
%T 13,7,2,3,2,3,2,2,3,2,2,2,3,2,2,3,7,2,2,3,2,3,7,7,2,3,11,2,3,7,2,2,2,
%U 3,43,7,7
%N Least prime p with 2*p^2 - 1 and 2*(n-p)^2 -1 both prime, or 0 if such a prime p does not exist.
%C Conjecture: 0 < a(n) < sqrt(2n)*(log n) except for n = 1, 2, 3, 232, 1478, 6457.
%C By the conjecture in the comments in A230351, 0 < a(n) < n for all n > 3.
%C Conjecture verified for n up to 10^9. - _Mauro Fiorentini_, Sep 22 2023
%H Zhi-Wei Sun, <a href="/A230362/b230362.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, preprint, arXiv:1211.1588 [math.NT], 2012-2017.
%e a(12) = 2 since 2*2^2 - 1 and 2*(12-2)^2 - 1 = 199 are both prime.
%t Do[Do[If[PrimeQ[2Prime[i]^2-1]&&PrimeQ[2(n-Prime[i])^2-1],Print[n," ",Prime[i]];Goto[aa]],{i,1,Max[13,PrimePi[n-1]]}];
%t Print[n," ",counterexample];Label[aa];Continue,{n,1,70}]
%Y Cf. A000040, A066049, A106483, A230351.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Oct 16 2013
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