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

1,1

Links

Table of n, a(n) for n=1..56.

Formula

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

Example

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

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 *)

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.

Sequence in context: A338450 A287273 A138828 * A257858 A095985 A270306

Adjacent sequences: A109309 A109310 A109311 * A109313 A109314 A109315

Keyword

nonn

Author

Zak Seidov, Jun 27 2005

Extensions

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

Status

approved