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

1,2

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.

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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.

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;

Crossrefs

Cf. A378898, A378946.

Sequence in context: A078724 A191022 A262958 * A155757 A027674 A124307

Adjacent sequences: A378942 A378943 A378944 * A378946 A378947 A378948

Keyword

nonn,more

Author

Robert Israel, Dec 11 2024

Status

approved