A358790 a(n) is the least prime p such that (2*n+1)^2 + p^2 is twice a prime.

3, 5, 3, 3, 5, 5, 3, 7, 3, 5, 5, 3, 3, 7, 5, 11, 5, 3, 7, 5, 5, 3, 13, 3, 5, 11, 3, 13, 5, 5, 5, 5, 7, 7, 5, 31, 5, 7, 3, 11, 19, 3, 3, 5, 11, 5, 5, 3, 7, 19, 5, 3, 11, 5, 5, 5, 3, 7, 5, 31, 5, 5, 3, 3, 19, 11, 3, 7, 5, 11, 41, 17, 13, 13, 5, 29, 5, 7, 3, 5, 5, 5, 13, 13, 5, 5, 3, 11, 13, 5, 19

Offset

0,1

Comments

If n == 0 or 4 (mod 5), a(n) == 0, 1 or 4 (mod 5).

If n == 1 or 3 (mod 5), a(n) == 0, 2 or 3 (mod 5).

If n == 2 (mod 5), a(n) == 1, 2, 3 or 4 (mod 5).

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

a(3) = 3 because 3 is prime, (2*3+1)^2 + 3^2 = 2*29 where 29 is prime, and no smaller prime than 3 works.

Maple

f:= proc(n) local s, p;
  s:= (2*n+1)^2; p:= 2;
  do
    p:= nextprime(p);
    if isprime((s+p^2)/2) then return p fi
  od
end proc:
map(f, [$0..100]);

Mathematica

a[n_] := Module[{p = 3}, While[! PrimeQ[((2*n + 1)^2 + p^2)/2], p = NextPrime[p]]; p]; Array[a, 100, 0] (* Amiram Eldar, Dec 01 2022 *)

Crossrefs

Sequence in context: A126659 A246917 A102294 * A021287 A124887 A304903

Adjacent sequences: A358787 A358788 A358789 * A358791 A358792 A358793

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 01 2022

Status

approved