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

4, 6, 12, 42, 60, 102, 150, 192, 282, 420, 432, 462, 570, 660, 810, 882, 1062, 1230, 1320, 1872, 1950, 2550, 2712, 2730, 3120, 3252, 4020, 4092, 6090, 8220, 8862, 8970, 9042, 9240, 9720, 10140, 10530, 10710, 11550, 11832, 11970, 12252, 13680, 13902

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

Sequence in context: A073167 A060202 A062624 * A050537 A114413 A068507

Adjacent sequences: A154663 A154664 A154665 * A154667 A154668 A154669

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Status

approved