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A154666 Numbers k such that k-1, k+1, and k^2-k-1 are primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 12:15 EDT 2022. Contains 356116 sequences. (Running on oeis4.)