A378945 Record values in A378898.

1, 5, 7, 13, 25, 27, 29, 31, 35, 41, 47, 53, 65, 73, 77, 103, 113, 119, 149, 179, 181, 215, 233, 235, 251, 319, 413, 425, 433, 455, 473, 485, 491, 529, 535, 557, 659, 725

Offset: 1

Author

Robert Israel, Dec 11 2024

Keywords

• nonn
• more

Comments

Numbers m > 0 such that for some k, (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.

The values of k are in A378946.

Examples

			a(1) = 1 = A378898(1), as (1+1)^2 + 1^2 = 5 is prime.
a(2) = 5 = A378898(3), as (5+3)^2 + 3^2 = 73 is prime, is the first value of A378898 greater than 1.
a(3) = 7 = A378898(13), as (7+13)^2 + 13^2 = 569 is prime, is the first value of A378898 greater than 5.
		

Crossrefs

Cf. A378898, A378946.

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:
R:= NULL: count:= 0: rec:= 0:
for k from 1 while count < 30 do
  v:= f(k);
  if v > rec then
    count:= count+1;
    R:= R, v;
    rec:= v;
  fi
od:
R;

Formula

a(n) = A378898(A378946(n)).