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

1,2

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.

Links

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

Formula

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

Example

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.

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;

Crossrefs

Cf. A378898, A378945.

Sequence in context: A171517 A179026 A179027 * A145907 A054554 A051939

Adjacent sequences: A378937 A378942 A378945 * A378951 A378952 A378953

Keyword

nonn,new

Author

Robert Israel, Dec 11 2024

Status

approved