A173085 Numbers k such that k, k^2 - 5, and k^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

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Keywords

• nonn
• changed

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

Crossrefs

Cf. A001358, A173082, A173083, A173084.

Programs

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 *)

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

Formula

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

Extensions

Edited by Charles R Greathouse IV, Apr 06 2010