A173085 Numbers n such that n, n^2 - 5, and n^2 + 5 are semiprime.

26, 62, 86, 118, 134, 566, 706, 982, 1198, 1322, 1346, 1678, 1706, 1822, 2386, 2402, 2498, 2654, 2966, 3086, 3142, 3158, 3326, 3662, 4222, 4874, 5158, 5354, 5774, 6602, 6638, 6746, 6998, 7142, 7586, 7646, 7834, 8006, 8482, 8486, 8846, 9134, 9406, 10558

Offset

1,1

Comments

26^2-5=671 -> 11*61, 26^2+5=681 -> 3*227,..

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) >> n log n. - Charles R Greathouse IV, Sep 14 2015

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-5; b=n^2+5; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 9!}]; lst
Select[Range[12000], PrimeOmega[#]==PrimeOmega[#^2-5] == PrimeOmega[ #^2+5] == 2&] (* Harvey P. Dale, Aug 29 2021 *)

Prog

(PARI) issemi(n)=bigomega(n)==2
is(n)=if(n%2, isprime((n^2-5)\2) && isprime((n^2+5)\2) && issemi(n), isprime(n/2) && issemi(n^2-5) && issemi(n^2+5)) \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A001358, A173082, A173083, A173084.

Sequence in context: A291105 A267294 A162316 * A044128 A044509 A039413

Adjacent sequences: A173082 A173083 A173084 * A173086 A173087 A173088

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Extensions

Edited by Charles R Greathouse IV, Apr 06 2010

Status

approved