cp's OEIS Frontend

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

%I A230515 #11 Sep 08 2022 08:46:06
%S A230515 2,3,5,6,9,11,15,20,38,39,45,48,50,54,59,93,126,131,144,149,153,174,
%T A230515 176,218,231,236,240,246,248,263,285,306,309,330,335,374,380,395,396,
%U A230515 401,419,423,449,455,468,471,474,495,501,506,549,551,560,588
%N A230515 Numbers n such that n*(n+1)-1 is a Sophie Germain prime.
%C A230515 This sequence is interesting because of the conjecture associated with A230514.
%H A230515 Zhi-Wei Sun, <a href="/A230515/b230515.txt">Table of n, a(n) for n = 1..10000</a>
%e A230515 a(1) = 2 since 2*3 - 1 = 5 is a Sophie Germain prime.
%e A230515 a(2) = 3 since 3*4 - 1 = 11 is a Sophie Germain prime.
%e A230515 a(3) = 5 since 5*6 - 1 = 29 is a Sophie Germain prime but 4*5 - 1 = 19 is not.
%t A230515 q[n_]:=PrimeQ[n(n+1)-1]&&PrimeQ[2n(n+1)-1]
%t A230515 m=0
%t A230515 Do[If[q[n],m=m+1;Print[m," ",n]],{n,1,506}]
%t A230515 Select[Range[600],AllTrue[{#^2+#-1,2#^2+2#-1},PrimeQ]&] (* _Harvey P. Dale_, Dec 02 2021 *)
%o A230515 (Magma) [n: n in [1..600] | IsPrime(n*(n+1)-1) and IsPrime(2*n*(n+1)-1)]; // _Bruno Berselli_, Oct 22 2013
%Y A230515 Cf. A000040, A005384, A230514.
%Y A230515 Subsequence of A045546.
%K A230515 nonn
%O A230515 1,1
%A A230515 _Zhi-Wei Sun_, Oct 21 2013