A378946 Locations of records in A378898.

1, 3, 13, 31, 49, 68, 216, 227, 288, 339, 408, 421, 797, 1176, 1494, 1947, 3876, 6453, 12108, 12558, 13272, 24027, 80667, 92472, 98154, 186543, 765351, 2294838, 6815886, 11105034, 12608001, 13669797, 25343472, 25485726, 40937853, 48562668, 72974013, 122175969

Offset: 1

Author

Robert Israel, Dec 11 2024

Keywords

• nonn

Comments

The record values are in A378945.

Numbers k such that for some m, (m+k)^2 + k^2 is prime while (m'+k)^2 + k^2 is not prime for 0 < m' < m, and for every k' < k there is m' < m such that (m'+k')^2 + k'^2 is prime.

Examples

			a(1) = 1, as A378898(1) = 1, with (1+1)^2 + 1^2 = 5 prime.
a(2) = 3, as A378898(3) = 5, with (5+3)^2 + 3^2 = 73 prime, and 3 is the first k with  A378898(k) > 1.
a(3) = 13, as A378898(13) = 7, with (7+13)^2 + 13^2 = 569 prime, and 13 is the first k with A378898(k) > 5.
		

Crossrefs

Cf. A378898, A378945.

Programs

Maple

f:= proc(k) local m;
  for m from 1 by 2 do
    if igcd(m,k) = 1 and isprime((k+m)^2 + k^2) then return m fi
  od
end proc:
J:= NULL: count:= 0: rec:= 0:
for k from 1 while count < 30 do
  v:= f(k);
  if v > rec then
    count:= count+1;
    J:= J, k;
    rec:= v;
  fi
od:
J;

Formula

A378898(a(n)) = A378945(n).