A184517 Upper s-Wythoff sequence, where s=4n-2. Complement of A184516.

3, 8, 14, 19, 24, 29, 35, 40, 45, 50, 55, 61, 66, 71, 76, 82, 87, 92, 97, 103, 108, 113, 118, 124, 129, 134, 139, 144, 150, 155, 160, 165, 171, 176, 181, 186, 192, 197, 202, 207, 213, 218, 223, 228, 234, 239, 244, 249, 254, 260, 265, 270, 275, 281, 286, 291, 296, 302, 307, 312, 317, 323, 328, 333, 338, 343, 349, 354, 359, 364, 370, 375, 380, 385, 391, 396, 401, 406, 412, 417, 422, 427, 432, 438, 443, 448, 453, 459, 464, 469, 474, 480, 485, 490, 495, 501, 506

Offset: 1

Author

Clark Kimberling, Jan 16 2011

Keywords

• nonn

Comments

See A184117 for the definition of lower and upper s-Wythoff sequences.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Clark Kimberling, Beatty Sequences and Wythoff Sequences, Generalized, Fibonacci Quart. 49 (2011), no. 3, 195-200.

Crossrefs

Cf. A184117, A184516.

Programs

Magma

[Floor((3+Sqrt(5))*(n - 1/(1+Sqrt(5)))): n in [1..100]]; // G. C. Greubel, Nov 16 2018

Mathematica

k = 4; r = 2; d = Sqrt[4 + k^2];
a[n_] := Floor[(1/2) (d + 2 - k) (n + r/(d + 2))];
b[n_] := Floor[(1/2) (d + 2 + k) (n - r/(d + 2))];
Table[a[n], {n, 120}] (* A184516 *)
Table[b[n], {n, 120}] (* A184517 *)
(* alternate program *)
Table[Ceiling[(2 n - 1) GoldenRatio^2], {n, 1, 120}] (* Jon Maiga, Nov 15 2018 *)

PARI

vector(100, n, floor((3+sqrt(5))*(n - 1/(1+sqrt(5))))) \\ G. C. Greubel, Nov 16 2018

Sage

[floor((3+sqrt(5))*(n - 1/(1+sqrt(5)))) for n in (1..100)] # G. C. Greubel, Nov 16 2018

Formula

a(n) = ceiling((2*n-1)*phi^2), where phi = A001622. - Jon Maiga, Nov 15 2018