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%I #24 Sep 08 2022 08:46:02
%S 1,2,3,1,5,24,7,8,1,10,99,12,13,56,135,4,425,8,4275,5,84,352,368,6,1,
%T 234,12,28,116,120,124,2,33,306,315,4,37,3800,156,10,6929,42,1075,176,
%U 45,184,47,3,1,2,204,117,1908,6,55,14,1425,58,236,60,10309,62
%N Least k such that 4*n*k+1 is a prime of the form m^2+1, or 0 if no such k exists.
%C Conjecture: a(n)>0. If the conjecture is true, then there exist infinitely many primes of the form m^2+1.
%H Alois P. Heinz and Charles R Greathouse IV, <a href="/A212275/b212275.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Heinz)
%p a:= proc(n) local k;
%p for k while not(isprime(4*n*k+1) and issqr (n*k)) do od; k
%p end:
%p seq (a(n), n=1..70); # _Alois P. Heinz_, May 13 2012
%o (PARI) a(n)=my(N=4*n*core(n),k=0);while(!isprime(k++^2*N+1),);k^2*N/(4*n) \\ _Charles R Greathouse IV_, May 14 2012
%o (Magma) S:=[]; for n in [1..62] do k:=1; while not IsPrime(4*n*k+1) or not IsSquare(n*k) do k:=k+1; end while; Append(~S, k); end for; S; // _Bruno Berselli_, May 15 2012
%Y Cf. A002496.
%K nonn,easy
%O 1,2
%A _Vladimir Shevelev_, May 13 2012
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