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%I #8 Jul 05 2018 11:00:54
%S 6,17,58,78,89,122,187,219,229,278,313,353,367,552,589,966,1162,1264,
%T 1530,1637,1745,1928,2343,2443,2540,2648,2789,3649,3778,3811,3900,
%U 4143,4191,5038,5228,5280,5426,5466,6169,6613,6718,7161,8225,9342,9607
%N Numbers n such that sum of n-th and (n+1)-st semiprimes is a square=q^2.
%F sp(n)+sp(n+1)=q^2, 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.
%t Position[Partition[Select[Range[40000],PrimeOmega[#]==2&],2,1],_?(IntegerQ[ Sqrt[Total[#]]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Jul 05 2018 *)
%o (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
%Y Values of q: A109312. 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 _Michel Marcus_, Oct 06 2013