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Numbers k such that (prime(k)^2 - 1)/6 - prime(k) is prime.
1

%I #14 Sep 09 2021 03:00:16

%S 7,8,12,13,17,20,24,25,28,29,32,39,42,45,52,53,58,59,63,64,67,72,75,

%T 79,83,87,88,93,100,102,114,115,125,126,127,131,139,140,144,154,159,

%U 160,173,180,190,195,219,223,232,234,240,248,253,265,278,279,284,296,299

%N Numbers k such that (prime(k)^2 - 1)/6 - prime(k) is prime.

%H G. C. Greubel, <a href="/A106630/b106630.txt">Table of n, a(n) for n = 1..1000</a>

%e (17^2 -1)/6 - 17 = 48 - 17 = 31 is prime, 17=prime(7), so 7 is a term.

%t Select[Range[350], PrimeQ[(Prime[#]^2 -6*Prime[#] -1)/6] &] (* _G. C. Greubel_, Sep 08 2021 *)

%o (PARI) is(n,p=prime(n))=isprime((p^2-1)/6-p) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A084922.

%K nonn

%O 1,1

%A _Pierre CAMI_, May 11 2005

%E a(12) corrected by _R. J. Mathar_, Nov 13 2009