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%I #10 Dec 11 2018 19:37:36
%S 6,10,19,22,24,28,35,38,39,43,46,49,50,62,64,83,92,96,106,110,114,120,
%T 133,136,139,142,146,168,171,172,174,180,181,199,203,204,207,208,222,
%U 230,232,240,258,276,280,288,289,294,300,304,310,321,325,326,327,328
%N Numbers q such that q^2 is a sum of n-th and (n+1)-st semiprimes for some n.
%F q^2=sp(n)+sp(n+1), sp(n)=n-th semiprime.
%e 6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.
%p isA001358 := proc(n) option remember ; if numtheory[bigomega](n) = 2 then true; else false ; fi ; end: isA118717 := proc(n) option remember ; local qn,qn1 ; qn := 4 ; while true do qn1 := qn+1 ; while not isA001358(qn1) do qn1 := qn1+1 ; od ; if qn+qn1 =n then RETURN(true) ; elif qn+qn1 > n then RETURN(false) ; fi; qn := qn1 ; od; end: isA109312 := proc(q) isA118717(q^2) ; end: for q from 1 to 500 do if isA109312(q) then printf("%d,",q) ; fi ; od; # _R. J. Mathar_, Aug 15 2007
%t Select[Sqrt[#]&/@(Total/@Partition[Select[Range[80000],PrimeOmega[#] == 2&],2,1]),IntegerQ] (* _Harvey P. Dale_, Dec 11 2018 *)
%Y Values of n: A109311. Cf. A001358 Semiprimes, A092191 Numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 27 2005
%E More terms from _R. J. Mathar_, Aug 15 2007
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