A342821 a(n) is the least prime p such that p*n+(n-1) and p*n-(n-1) are both prime, or 0 if there is no such p.

2, 2, 3, 2, 3, 2, 5, 3, 5, 2, 3, 29, 7, 0, 3, 2, 0, 2, 11, 3, 3, 5, 0, 19, 5, 3, 29, 2, 0, 2, 13, 0, 3, 29, 3, 2, 41, 0, 5, 11, 3, 11, 5, 0, 5, 2, 0, 3, 5, 3, 19, 19, 3, 11, 7, 3, 11, 2, 0, 2, 7, 0, 3, 5, 0, 2, 5, 3, 11, 5, 0, 19, 13, 0, 31, 7, 0, 2, 19, 0, 7, 11, 3, 5, 19, 0, 5, 2, 0, 3, 7, 0, 5

Offset

1,1

Comments

If n == 2 (mod 3) then a(n) <= 3.

Links

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

Example

a(7) = 5 because 5*7+6 = 41 and 5*7-6 = 29 are prime, and 5 is the least prime that works.

Maple

f:= proc(n) local p, pmax;
  p:= 1:
  if n mod 3 = 2 then pmax := 3 else pmax := infinity fi;
  while p < pmax do
    p:= nextprime(p);
    if isprime(n*p+n-1) and isprime(n*p-n+1) then return p fi;
  od:
  0
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A342822.

Sequence in context: A331597 A356231 A339502 * A165916 A096013 A072380

Adjacent sequences: A342818 A342819 A342820 * A342822 A342823 A342824

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 25 2021

Status

approved