A351848 a(n) is the least prime p such that k*(p^2-1)+2*n+1 is prime for k=1..2*n, or 0 if there is no such p.

3, 7, 423281, 0

Offset

1,1

Comments

If n == 1 (mod 3) and n > 1, then a(n) = 0.

a(5) > 10^10 if it is not 0.

Links

Table of n, a(n) for n=1..4.

Example

a(2) = 7 because 5 + 1*(7^2-1) = 53, 5 + 2*(7^2-1) = 101, 5 + 3*(7^2-1) = 149 and 5 + 4*(7^2-1) = 197 are all prime.

Maple

f:= proc(n) local p, pmax, k;
  if n mod 3 = 1 then
    if n=1 then return 3 else return 0 fi
  fi;
  p:= 1:
  while p < 10^8 do
    p:= nextprime(p);
    if andmap(isprime, [seq(k*(p^2-1)+2*n+1, k=1..2*n)]) then return p fi
  od;
FAIL
end proc:
map(f, [$1..5]);

Crossrefs

Sequence in context: A083461 A137029 A174307 * A137125 A103319 A341812

Adjacent sequences: A351845 A351846 A351847 * A351849 A351850 A351851

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Feb 21 2022

Status

approved