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A230515
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Numbers n such that n*(n+1)-1 is a Sophie Germain prime.
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2
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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
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OFFSET
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1,1
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COMMENTS
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This sequence is interesting because of the conjecture associated with A230514.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(Magma) [n: n in [1..600] | IsPrime(n*(n+1)-1) and IsPrime(2*n*(n+1)-1)]; // Bruno Berselli, Oct 22 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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