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 A180656 Squarefree semiprimes k such that (m+1)^2-k is also a square, where m = ceiling(sqrt(k)). 0
 33, 39, 85, 119, 133, 253, 377, 403, 527, 629, 703, 943, 989, 1363, 1537, 1643, 2183, 2257, 2747, 2881, 3053, 3139, 3337, 3431, 4187, 4399, 4897, 5251, 5429, 6499, 6767, 6887, 6901, 7171, 7313, 7373, 7519, 7597, 7811, 7957, 8453, 8611, 8927, 9379, 11303 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Original name: Squarefree semiprimes k such that the second-next perfect square minus k is a perfect square. LINKS Table of n, a(n) for n=1..45. 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 Cf. A006881, A180655. Sequence in context: A039326 A043149 A043929 * A034070 A168311 A045241 Adjacent sequences: A180653 A180654 A180655 * A180657 A180658 A180659 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

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Last modified February 28 02:34 EST 2024. Contains 370379 sequences. (Running on oeis4.)