The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A259726 Numbers k such that [r[s*k]] > [s[r*k]], where r = sqrt(2), s=sqrt(3), and [ ] = floor. 3
 2, 3, 6, 7, 9, 11, 12, 14, 26, 33, 36, 40, 41, 43, 48, 52, 55, 59, 62, 65, 67, 70, 72, 74, 77, 82, 84, 89, 91, 93, 94, 96, 101, 108, 111, 115, 118, 119, 122, 123, 125, 130, 134, 137, 140, 141, 144, 147, 148, 149, 151, 152, 154, 159, 164, 171, 175, 178, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that r and s are distinct real numbers, and let f(r,s,k) = [s[r*k]] - [r[s*k]]. Let (G(n)) be the sequence of those k for which f(r,s,k) > 0, let (E(n)) be those for which f(r,s,k) = 0, and (L(n)), those for which f(r,s,k) < 0. Clearly (G(n)), E(n)), L(n)) partition the positive integers. Conjecture: the limits g = lim G(n)/n, e = lim E(n)/n, el = lim L(n) exist; if so, then 1/g + 1/e + 1/el = 1.) In particular, A259724, A259725 and A259726 partition the positive integers. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 MATHEMATICA z = 1000; r = Sqrt; s = Sqrt; u = Table[Floor[r*Floor[s*n]], {n, 1, z}]; v = Table[Floor[s*Floor[r*n]], {n, 1, z}]; Select[Range, u[[#]] < v[[#]] &]  (* A259724 *) Select[Range, u[[#]] == v[[#]] &] (* A259725 *) Select[Range, u[[#]] > v[[#]] &]  (* A259726 *) CROSSREFS Cf. A259724, A259745. Sequence in context: A201734 A287775 A283208 * A259587 A304107 A181732 Adjacent sequences:  A259723 A259724 A259725 * A259727 A259728 A259729 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 15 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 27 18:40 EDT 2020. Contains 337386 sequences. (Running on oeis4.)