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A070552 Semiprimes k such that k+1 is also a semiprime.

%I A070552 #39 Sep 08 2022 08:45:05
%S A070552 9,14,21,25,33,34,38,57,85,86,93,94,118,121,122,133,141,142,145,158,
%T A070552 177,201,202,205,213,214,217,218,253,298,301,302,326,334,361,381,393,
%U A070552 394,445,446,453,481,501,514,526,537,542,553,565,622,633,634,694,697
%N A070552 Semiprimes k such that k+1 is also a semiprime.
%C A070552 A064911(a(n))*A064911(a(n)+1) = 1. - _Reinhard Zumkeller_, Dec 03 2009
%H A070552 D. W. Wilson, <a href="/A070552/b070552.txt">Table of n, a(n) for n = 1..10000</a>
%F A070552 a(n) >> n log n since either n or n+1 is in A100484. - _Charles R Greathouse IV_, Jul 21 2015
%F A070552 a(n) = A109373(n) - 1. - _Zak Seidov_ Dec 19 2018
%t A070552 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 A070552 Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,700}],2,1],{1,1}]] (* _Harvey P. Dale_, Feb 04 2015 *)
%t A070552 Select[Range[700], PrimeOmega[#] == PrimeOmega[# + 1] == 2 &] (* _Vincenzo Librandi_, Jan 22 2016 *)
%o A070552 (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 A070552 (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 A070552 (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
%o A070552 (Python)
%o A070552 from sympy import factorint
%o A070552 def is_semiprime(n): return sum(e for e in factorint(n).values()) == 2
%o A070552 def ok(n): return is_semiprime(n) and is_semiprime(n+1)
%o A070552 print(list(filter(ok, range(698)))) # _Michael S. Branicky_, Sep 14 2021
%Y A070552 Cf. A001358, A007674, A039832, A100484.
%K A070552 nonn
%O A070552 1,1
%A A070552 Sharon Sela (sharonsela(AT)hotmail.com), May 03 2002
%E A070552 More terms from _Vladeta Jovovic_, May 03 2002