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A092207 Semiprimes k such that k+2 is also a semiprime.

%I A092207 #34 Feb 16 2025 08:32:52
%S A092207 4,33,49,55,85,91,93,119,121,141,143,159,183,185,201,203,213,215,217,
%T A092207 219,235,247,265,287,289,299,301,303,319,321,327,339,391,393,411,413,
%U A092207 415,445,451,469,471,515,517,527,533,535,543,551,579,581,589,633,667
%N A092207 Semiprimes k such that k+2 is also a semiprime.
%C A092207 Starting with 33 all terms are odd. First squares are 4, 49, 169, 361, 529, 961, 1369, 2209, 2809, 4489, ... - _Zak Seidov_, Feb 17 2017
%H A092207 Zak Seidov, <a href="/A092207/b092207.txt">Table of n, a(n) for n = 1..10000</a>
%H A092207 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%t A092207 PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 668], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # + 2] == 2 &]
%t A092207 Select[Range[700],PrimeOmega[#]==PrimeOmega[#+2]==2&] (* _Harvey P. Dale_, Aug 20 2011 *)
%t A092207 SequencePosition[Table[If[PrimeOmega[n]==2,1,0],{n,700}],{1,_,1}] [[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 29 2017 *)
%o A092207 (PARI) is(n)=if(n%2==0, return(n==4)); bigomega(n)==2 && bigomega(n+2)==2 \\ _Charles R Greathouse IV_, Feb 21 2017
%o A092207 (Python)
%o A092207 from sympy import factorint
%o A092207 from itertools import count, islice
%o A092207 def agen(): # generator of terms
%o A092207     yield 4
%o A092207     nxt = 0
%o A092207     for k in count(5, 2):
%o A092207         prv, nxt = nxt, sum(factorint(k+2).values())
%o A092207         if prv == nxt == 2: yield k
%o A092207 print(list(islice(agen(), 53))) # _Michael S. Branicky_, Nov 26 2022
%Y A092207 Cf. A056809, A070552, A092125, A092126, A092127, A092128, A092129, A082919, A092209.
%K A092207 nonn
%O A092207 1,1
%A A092207 _Robert G. Wilson v_ and _Zak Seidov_, Feb 24 2004