A230515 Numbers n such that n*(n+1)-1 is a Sophie Germain prime.

2, 3, 5, 6, 9, 11, 15, 20, 38, 39, 45, 48, 50, 54, 59, 93, 126, 131, 144, 149, 153, 174, 176, 218, 231, 236, 240, 246, 248, 263, 285, 306, 309, 330, 335, 374, 380, 395, 396, 401, 419, 423, 449, 455, 468, 471, 474, 495, 501, 506, 549, 551, 560, 588

Offset

1,1

Comments

This sequence is interesting because of the conjecture associated with A230514.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 2 since 2*3 - 1 = 5 is a Sophie Germain prime.
a(2) = 3 since 3*4 - 1 = 11 is a Sophie Germain prime.
a(3) = 5 since 5*6 - 1 = 29 is a Sophie Germain prime but 4*5 - 1 = 19 is not.

Mathematica

q[n_]:=PrimeQ[n(n+1)-1]&&PrimeQ[2n(n+1)-1]
m=0
Do[If[q[n], m=m+1; Print[m, " ", n]], {n, 1, 506}]
Select[Range[600], AllTrue[{#^2+#-1, 2#^2+2#-1}, PrimeQ]&] (* Harvey P. Dale, Dec 02 2021 *)

Prog

(Magma) [n: n in [1..600] | IsPrime(n*(n+1)-1) and IsPrime(2*n*(n+1)-1)]; // Bruno Berselli, Oct 22 2013

Crossrefs

Cf. A000040, A005384, A230514.

Subsequence of A045546.

Sequence in context: A309830 A008770 A347548 * A030068 A239958 A008769

Adjacent sequences: A230512 A230513 A230514 * A230516 A230517 A230518

Keyword

nonn

Author

Zhi-Wei Sun, Oct 21 2013

Status

approved