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A154666 Numbers k such that k-1, k+1, and k^2-k-1 are primes. 3

%I

%S 4,6,12,42,60,102,150,192,282,420,432,462,570,660,810,882,1062,1230,

%T 1320,1872,1950,2550,2712,2730,3120,3252,4020,4092,6090,8220,8862,

%U 8970,9042,9240,9720,10140,10530,10710,11550,11832,11970,12252,13680,13902

%N Numbers k such that k-1, k+1, and k^2-k-1 are primes.

%C Note that k-1 and k+1 are twin primes and the third prime is (k-1)*(k+1)-k, the product of the twin primes minus their average.

%H Amiram Eldar, <a href="/A154666/b154666.txt">Table of n, a(n) for n = 1..10000</a>

%e 3*5 - 4 = 11.

%e 5*7 - 6 = 29.

%t lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],If[PrimeQ[(n-1)*(n+1)-n],AppendTo[lst,n]]],{n,8!}];lst

%t Mean/@Select[Select[Partition[Prime[Range[2000]],2,1],Last[#]-First[#]==2&], PrimeQ[Times@@#-Mean[#]]&] (* _Harvey P. Dale_, Mar 17 2011 *)

%o (Magma) [k:k in [2..15000]| IsPrime(k-1) and IsPrime(k+1)and IsPrime(k^2-k-1)]; // _Marius A. Burtea_, Dec 21 2019

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009

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Last modified September 29 16:23 EDT 2022. Contains 357090 sequences. (Running on oeis4.)