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A161868
Primes p such that both p+2 and p-2 are products of 3 distinct primes.
1
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
OFFSET
1,1
COMMENTS
None of the 3 distinct primes may have an exponent other than 1. - Harvey P. Dale, Dec 25 2022
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition rephrased by R. J. Mathar, Jun 23 2009
STATUS
approved