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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
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
Sequence in context: A039326 A043149 A043929 * A034070 A168311 A045241
KEYWORD
nonn
AUTHOR
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.)