A389884 Numbers k such that k^2 + 1 is a Sophie Germain prime.

1, 2, 40, 110, 160, 170, 250, 440, 490, 890, 910, 950, 1070, 1210, 1640, 1660, 1990, 2050, 2080, 2360, 2420, 2470, 3290, 3520, 3890, 4370, 4850, 5180, 5930, 6130, 6350, 7100, 7810, 7910, 8350, 8500, 8540, 8680, 8720, 10520, 10640, 11270, 11830, 12140, 12620

Offset

1,2

Comments

We observe that a(n)==0 (mod 10) for n>2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1)=1 is a term because 1^2+1 = 2 = A005384(1),
a(2)=2 is a term because 2^2+1 = 5 = A005384(3),
a(3)=40 is a term because 40^2+1 = 1601 = A005384(54).

Maple

nn:=15000 :
for k from 1 to nn do :
 p:=k^2+1 :
  if isprime(p) and isprime(2*p+1)
   then printf(`%d, `, k):
  fi:
od:

Mathematica

okQ[k_]:=PrimeQ[k^2+1]&&PrimeQ[2(k^2+1)+1]; Select[Range[12620], okQ] (* James C. McMahon, Nov 24 2025 *)

Crossrefs

Subsequence of A005574.

Cf. A005384.

Sequence in context: A275547 A387088 A269544 * A281761 A370069 A385356

Adjacent sequences: A389881 A389882 A389883 * A389885 A389886 A389887

Keyword

nonn,changed

Author

Michel Lagneau, Nov 18 2025

Status

approved