A345469 a(n) is the least k such that A345468(k) = 2*n-1.

1, 2, 12, 6, 14, 30, 111, 74, 117, 198, 89, 336, 174, 116, 489, 264, 101, 1251, 2730, 308, 3219, 4836, 1274, 2466, 3999, 1130, 7266, 15571, 440, 3225, 4989, 866, 4674, 8916, 1154, 22395, 24786, 1226, 30126, 26439, 3110, 26781, 27366, 3191, 4149, 12729, 446, 54759, 26946, 3779, 16044, 26841, 4301

Offset

1,2

Comments

a(n) is the least k such that (2*n-1)^2+4*k is prime but (2*m-1)^2+4*k is composite for all m from 1 to n-1.

Links

Table of n, a(n) for n=1..53.

Example

a(4) = 6 because 2*4-1 = 7 and 7^2+4*6 = 73 is prime but 1^2+4*6 = 25, 3^2+4*6 = 33 and 5^2+4*6=49 are not.

Maple

f:= proc(n) local k, m;
  m:= 4*n;
  for k from 1 by 2 do
    if isprime(k^2+m) then return k fi
  od
end proc:
V:= Vector(119):
count:= 0:
for n from 1 while count < 60 do
  v:= f(n);
  if v <= 119 and V[v]=0 then V[v]:= n; count:= count+1 fi
od:
seq(V[2*i-1], i=1..60);

Crossrefs

Cf. A345468.

Sequence in context: A079080 A228454 A278255 * A035877 A086494 A354484

Adjacent sequences: A345466 A345467 A345468 * A345470 A345471 A345472

Keyword

nonn

Author

Robert Israel, Jun 20 2021

Status

approved