OFFSET
1,1
COMMENTS
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
3*5 - 4 = 11.
5*7 - 6 = 29.
MATHEMATICA
lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], If[PrimeQ[(n-1)*(n+1)-n], AppendTo[lst, n]]], {n, 8!}]; lst
Mean/@Select[Select[Partition[Prime[Range[2000]], 2, 1], Last[#]-First[#]==2&], PrimeQ[Times@@#-Mean[#]]&] (* Harvey P. Dale, Mar 17 2011 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 13 2009
STATUS
approved