OFFSET
1,1
COMMENTS
Original name: Squarefree semiprimes k such that the second-next perfect square minus k is a perfect square.
EXAMPLE
3*11 = 33, 49-33 = 16 -> 4, 7-4 = 3, 7+4 = 11;
3*13 = 39, 64-39 = 25 -> 5, 8-5 = 3, 8+5 = 13.
MATHEMATICA
f1[n_] := Last/@FactorInteger[n] == {1, 1}; f2[n_] := IntegerQ[Sqrt[(Ceiling[Sqrt[n]] + 1)^2 - n]]; lst={}; Do[If[f1[n] && f2[n], AppendTo[lst, n]], {n, 8!}]; lst
Select[Range[12000], PrimeOmega[#]==2&&SquareFreeQ[#]&&IntegerQ[Sqrt[ (Ceiling[ Sqrt[#]]+1)^2-#]]&] (* Harvey P. Dale, Mar 17 2023 *)
PROG
(PARI) isok(k) = issquarefree(k) && (bigomega(k)==2) && issquare((ceil(sqrt(k))+1)^2-k); \\ Michel Marcus, Nov 27 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 15 2010
EXTENSIONS
Original name replaced (using an Apr 19 2012 Comments entry from M. F. Hasler) by Jon E. Schoenfield, Nov 25 2019
STATUS
approved