A344463 a(n) is the least prime p such that (p^2-2*n)/(2*n-1) and (p^2+2*n)/(2*n+1) are both prime, or 0 if such p does not exist.

2, 0, 239, 251, 2069, 131, 521, 0, 2243, 379, 643, 40849, 89101, 11717, 81839, 18787, 659, 0, 2887, 41081, 199261, 13931, 4231, 223439, 17443, 953, 3499, 6689, 122131, 298777, 9883, 0, 93131, 12329, 48989, 67307, 9199, 44549, 13903, 294353, 605071, 42331, 7309, 167677, 41651, 46747, 129581

Offset

1,1

Comments

a(n) = 0 if 2*n is a square.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 239 because 239, (239^2-2*3)/(2*3-1) = 11423, and (239^2+2*3)/(2*3+1) = 8161 are primes, and no smaller prime works.

Maple

f:= proc(n) local M, p, i, j;
  if issqr(2*n) then return 0 fi;
  M:= sort(map(t -> rhs(op(t)), [msolve(p^2=1, 4*n^2-1)]));
  for i from 0 to 10^6 do
    for j in M do
      p:= i*(4*n^2-1)+j;
      if isprime(p) and isprime((p^2-2*n)/(2*n-1)) and  isprime((p^2+2*n)/(2*n+1)) then return p fi
  od od;
  FAIL
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A001105.

Sequence in context: A037096 A111814 A036938 * A221750 A284451 A348183

Adjacent sequences: A344460 A344461 A344462 * A344464 A344465 A344466

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 19 2021

Status

approved