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A109312
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Numbers q such that q^2 is a sum of n-th and (n+1)-st semiprimes for some n.
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1
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6, 10, 19, 22, 24, 28, 35, 38, 39, 43, 46, 49, 50, 62, 64, 83, 92, 96, 106, 110, 114, 120, 133, 136, 139, 142, 146, 168, 171, 172, 174, 180, 181, 199, 203, 204, 207, 208, 222, 230, 232, 240, 258, 276, 280, 288, 289, 294, 300, 304, 310, 321, 325, 326, 327, 328
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OFFSET
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1,1
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LINKS
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FORMULA
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q^2=sp(n)+sp(n+1), sp(n)=n-th semiprime.
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EXAMPLE
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6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.
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MAPLE
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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
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MATHEMATICA
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Select[Sqrt[#]&/@(Total/@Partition[Select[Range[80000], PrimeOmega[#] == 2&], 2, 1]), IntegerQ] (* Harvey P. Dale, Dec 11 2018 *)
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CROSSREFS
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Values of n: A109311. Cf. A001358 Semiprimes, A092191 Numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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