A109311 Numbers n such that sum of n-th and (n+1)-st semiprimes is a square=q^2.

6, 17, 58, 78, 89, 122, 187, 219, 229, 278, 313, 353, 367, 552, 589, 966, 1162, 1264, 1530, 1637, 1745, 1928, 2343, 2443, 2540, 2648, 2789, 3649, 3778, 3811, 3900, 4143, 4191, 5038, 5228, 5280, 5426, 5466, 6169, 6613, 6718, 7161, 8225, 9342, 9607

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 q: A109312. Cf. A001358 = semiprimes, A092191 = numbers n such that sum of n-th and (n+1)-st semiprimes is a semiprime.

Programs

Mathematica

Position[Partition[Select[Range[40000],PrimeOmega[#]==2&],2,1],?(IntegerQ[ Sqrt[Total[#]]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, Jul 05 2018 *)

PARI

lista(nn) = {vec = vector(nn, i, i); sp = select(i->(bigomega(i)==2), vec); for (i = 1, #sp-1, if (issquare(sp[i+1]+sp[i]), print1(i, ", ")););} \\ Michel Marcus, Oct 06 2013

Formula

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

Extensions

More terms from Michel Marcus, Oct 06 2013