A390482 Least positive integer k such that (2^n*k)^2+1 is prime, or 0 if no such k exists.

1, 1, 1, 2, 1, 5, 4, 2, 1, 10, 5, 5, 25, 13, 14, 7, 9, 17, 9, 12, 6, 3, 11, 18, 9, 10, 5, 7, 80, 40, 20, 10, 5, 7, 79, 63, 40, 20, 10, 5, 15, 22, 11, 15, 25, 57, 44, 22, 11, 38, 19, 15, 9, 258, 129, 98, 49, 28, 14, 7, 46, 23, 46, 23, 24, 12, 6, 3, 91, 97, 66, 33, 29

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..3007

Formula

a(n) = A193807(4^n). - Robert Israel, Jun 11 2026

Example

a(0)=1 because (2^0*1)^2+1 = 2 is prime.
a(3)=2 because (2^3*2)^2+1 = 257 is prime.
a(5)=5 because (2^5*5)^2+1 = 25601 is prime.

Maple

nn:=10^6:
for n from 0 to 72 do:
ii:=0:
 for k from 0 to nn while (ii=0) do:
   if isprime((2^n*k)^2+1) then ii:=1:printf(`%d, `, k):
    else
   fi :
 od:
  if ii=0 then printf(`%d, `, 0):
   else
  fi:
od:

Mathematica

a[n_] := Module[{k = 1}, While[!PrimeQ[(2^n*k)^2 + 1], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Nov 07 2025 *)

Prog

(PARI) a(n) = my(k=1); while (!ispseudoprime((2^n*k)^2+1), k++); k; \\ Michel Marcus, Nov 07 2025

Crossrefs

Cf. A002496, A052292, A193807, A389785.

Sequence in context: A248669 A103718 A113350 * A227372 A395740 A359131

Adjacent sequences: A390479 A390480 A390481 * A390483 A390484 A390485

Keyword

nonn

Author

Michel Lagneau, Nov 07 2025

Status

approved