A356077 a(n) is the least prime p such that 2*n - p^2 is prime, or -1 if there is no such p.

-1, -1, 2, -1, -1, 3, 3, 3, -1, 3, 3, -1, 3, 3, 5, 3, -1, 5, 3, 3, 5, 5, 3, 5, 3, 3, 5, 3, -1, 7, 3, -1, 5, 3, 3, 5, -1, 3, 5, 3, 3, 5, 5, 3, 7, 3, -1, 5, 3, -1, 7, 5, 3, 5, 3, 3, 5, 3, 3, 7, 3, 11, 5, 5, -1, 5, 5, 3, 5, 3, -1, 11, 3, 3, 7, 5, -1, 5, 3, 3, 5, 5, 3, 11, -1, 3, 5, 3, -1, 7, 3, -1

Offset

1,3

Comments

If n == 2 (mod 3), then a(n) is either -1, 3, or sqrt(n-3).

If 2*n is a square, then a(n) is either -1 or sqrt(2*n)-1 (in which case a(n) must be in A005384).

Links

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

Example

a(7) = 3 because 2*7 - 3^2 = 5 is prime.

Maple

f:= proc(n) local p;
  if n mod 3 = 2 then
    if isprime(2*n-3^2) then return 3
    elif issqr(2*n-3) and isprime(sqrt(2*n-3)) then return sqrt(2*n-3)
    else return -1
  fi fi;
  p:= 1:
  while p^2 < 2*n do
    p:= nextprime(p);
    if isprime(2*n-p^2) then return p fi
  od;
  -1
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A005384, A356108.

Sequence in context: A279677 A262180 A308028 * A320902 A189913 A240807

Adjacent sequences: A356074 A356075 A356076 * A356078 A356079 A356080

Keyword

sign

Author

J. M. Bergot and Robert Israel, Jul 27 2022

Status

approved