A173996 Primes p such that both (p-1)*(p-2) and (p+1)*(p+2) are averages of twin prime pairs.

5, 7, 23, 161957, 180287, 484153, 496123, 610633, 799223, 805523, 1466747, 1489507, 1562983, 1857287, 2331887, 2398223, 2550203, 2599847, 2728703, 3562043, 3752093, 4094743, 4366847, 4451743, 4914653, 5137547, 5378497, 6305857, 6709057, 6718763, 6797933, 6930037

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

5 is a term since (5-1)*(5-2) = 4*3 = 12 and (5+1)*(5+2) = 6*7 = 42 are averages of the twin prime pairs (11, 13) and (41, 43).
7 is a term since (7-1)*(7-2) = 6*5 = 30 and (7+1)*(7+2) = 8*9 = 72 are averages of the twin prime pairs (29, 31) and (71, 73).

Mathematica

f[n_]:=PrimeQ[(n-1)*(n-2)-1]&&PrimeQ[(n-1)*(n-2)+1]&&PrimeQ[(n+1)*(n+2)-1]&&PrimeQ[(n+1)*(n+2)+1]; lst={}; Do[p=Prime[n]; If[f[p], AppendTo[lst, p]], {n, 9!}]; lst
Select[Prime[Range[475000]], AllTrue[{(#-1)(#-2)-1, (#-1)(#-2)+1, (#+1) (#+2)- 1, (#+1)(#+2)+1}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 14 2020 *)

Crossrefs

Cf. A014574.

Sequence in context: A121605 A226657 A229021 * A024864 A025108 A298900

Adjacent sequences: A173993 A173994 A173995 * A173997 A173998 A173999

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 04 2010

Extensions

More terms from Amiram Eldar, Dec 22 2019

Status

approved