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

Author

Zhi-Wei Sun, Oct 21 2013

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A005384, A230514.

Subsequence of A045546.

Programs

Magma

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

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 *)