A161868 - OEIS

A161868

Primes p such that both p+2 and p-2 are products of 3 distinct primes.

1237, 1493, 1549, 1597, 2137, 2753, 2767, 2917, 3533, 3617, 4013, 4253, 4919, 5557, 5683, 5693, 5783, 6151, 6353, 6367, 6917, 6967, 6983, 7057, 7187, 7537, 7687, 7703, 7883, 8101, 8167, 8243, 8447, 8699, 8731, 8963, 9697, 9739, 9787, 9833, 9887, 10151

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OFFSET

1,1

COMMENTS

None of the 3 distinct primes may have an exponent other than 1. - Harvey P. Dale, Dec 25 2022

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

1237-2=5*13*19. 1237+2=3*7*59. 1493-2=3*7*71. 1493+2=5*13*23.

MATHEMATICA

fQ[n_]:=Last/@FactorInteger[n]=={1, 1, 1}; q=2; lst={}; Do[p=Prime[n]; If[fQ[p-q]&&fQ[p+q], AppendTo[lst, p]], {n, 7!}]; lst

Select[Prime[Range[1250]], FactorInteger[#+2][[All, 2]]== FactorInteger[ #-2] [[All, 2]]=={1, 1, 1}&] (* Harvey P. Dale, Aug 03 2016 *)

Select[Prime[Range[1250]], PrimeNu[#+{2, -2}]==PrimeOmega[#+{2, -2}] == {3, 3}&] (* Harvey P. Dale, Dec 25 2022 *)

CROSSREFS

Cf. A007304. [R. J. Mathar, Jun 23 2009]

Sequence in context: A210515 A122043 A179913 * A145047 A236974 A237552

Adjacent sequences: A161865 A161866 A161867 * A161869 A161870 A161871

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

EXTENSIONS

Definition rephrased by R. J. Mathar, Jun 23 2009

STATUS

approved