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 A070552 Numbers n such that n and n+1 are semiprimes. 28

%I

%S 9,14,21,25,33,34,38,57,85,86,93,94,118,121,122,133,141,142,145,158,

%T 177,201,202,205,213,214,217,218,253,298,301,302,326,334,361,381,393,

%U 394,445,446,453,481,501,514,526,537,542,553,565,622,633,634,694,697

%N Numbers n such that n and n+1 are semiprimes.

%C A064911(a(n))*A064911(a(n)+1) = 1. - _Reinhard Zumkeller_, Dec 03 2009

%H D. W. Wilson, <a href="/A070552/b070552.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) >> n log n since either n or n+1 is in A100484. - _Charles R Greathouse IV_, Jul 21 2015

%F a(n) = A109373(n) - 1. - _Zak Seidov_ Dec 19 2018

%t f[n_]:=Last/@FactorInteger[n]=={1,1}||Last/@FactorInteger[n]=={2};lst={};Do[If[f[n]&&f[n+1],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 25 2010 *)

%t Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,700}],2,1],{1,1}]] (* _Harvey P. Dale_, Feb 04 2015 *)

%t Select[Range[700], PrimeOmega[#] == PrimeOmega[# + 1] == 2 &] (* _Vincenzo Librandi_, Jan 22 2016 *)

%o (PARI) forprime(p=3,1e3,if(bigomega(2*p-1)==2,print1(2*p-1", "));if(bigomega(2*p+1)==2,print1(2*p", "))) \\ _Charles R Greathouse IV_, Nov 09 2011

%o (PARI) is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2, isprime(n/2) && bigomega(n+1)==2) \\ _Charles R Greathouse IV_, Sep 08 2015

%o (MAGMA) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..700] | IsSemiprime(n) and IsSemiprime(n+1) ]; // _Vincenzo Librandi_, Jan 22 2016

%Y Cf. A001358, A007674, A039832, A100484.

%K nonn

%O 1,1

%A Sharon Sela (sharonsela(AT)hotmail.com), May 03 2002

%E More terms from _Vladeta Jovovic_, May 03 2002

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Last modified July 20 05:56 EDT 2019. Contains 325168 sequences. (Running on oeis4.)