A212275 Least k such that 4*n*k+1 is a prime of the form m^2+1, or 0 if no such k exists.

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, 234, 12, 28, 116, 120, 124, 2, 33, 306, 315, 4, 37, 3800, 156, 10, 6929, 42, 1075, 176, 45, 184, 47, 3, 1, 2, 204, 117, 1908, 6, 55, 14, 1425, 58, 236, 60, 10309, 62

Offset

1,2

Comments

Conjecture: a(n)>0. If the conjecture is true, then there exist infinitely many primes of the form m^2+1.

Links

Alois P. Heinz and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Heinz)

Maple

a:= proc(n) local k;
      for k while not(isprime(4*n*k+1) and issqr (n*k)) do od; k
    end:
seq (a(n), n=1..70);  # Alois P. Heinz, May 13 2012

Prog

(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
(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

Crossrefs

Cf. A002496.

Sequence in context: A231733 A182822 A137211 * A189036 A319952 A174665

Adjacent sequences: A212272 A212273 A212274 * A212276 A212277 A212278

Keyword

nonn,easy

Author

Vladimir Shevelev, May 13 2012

Status

approved