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%I #10 Aug 29 2021 11:04:33
%S 26,62,86,118,134,566,706,982,1198,1322,1346,1678,1706,1822,2386,2402,
%T 2498,2654,2966,3086,3142,3158,3326,3662,4222,4874,5158,5354,5774,
%U 6602,6638,6746,6998,7142,7586,7646,7834,8006,8482,8486,8846,9134,9406,10558
%N Numbers n such that n, n^2 - 5, and n^2 + 5 are semiprime.
%C 26^2-5=671 -> 11*61, 26^2+5=681 -> 3*227,..
%H Charles R Greathouse IV, <a href="/A173085/b173085.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) >> n log n. - _Charles R Greathouse IV_, Sep 14 2015
%t 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
%t Select[Range[12000],PrimeOmega[#]==PrimeOmega[#^2-5] == PrimeOmega[ #^2+5] == 2&] (* _Harvey P. Dale_, Aug 29 2021 *)
%o (PARI) issemi(n)=bigomega(n)==2
%o 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
%Y Cf. A001358, A173082, A173083, A173084.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 09 2010
%E Edited by _Charles R Greathouse IV_, Apr 06 2010