A109312 Numbers q such that q^2 is a sum of n-th and (n+1)-st semiprimes for some n.

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

Offset: 1

Author

Zak Seidov, Jun 27 2005

Keywords

• nonn

Examples

			6 is ok because sp(6)=15, sp(7)=21, 15+21=36=6^2, sp(n)=A001358(n)=n-th semiprime.
		

Crossrefs

Values of n: A109311. Cf. A001358 Semiprimes, A092191 Numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

Maple

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

Mathematica

Select[Sqrt[#]&/@(Total/@Partition[Select[Range[80000],PrimeOmega[#] == 2&],2,1]),IntegerQ] (* Harvey P. Dale, Dec 11 2018 *)

Formula

q^2=sp(n)+sp(n+1), sp(n)=n-th semiprime.

Extensions

More terms from R. J. Mathar, Aug 15 2007