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

1,1

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.

Formula

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

Prog

(PARI) vector(100, n, floor((3+sqrt(5))*(n - 1/(1+sqrt(5))))) \\ G. C. Greubel, Nov 16 2018
(Magma) [Floor((3+Sqrt(5))*(n - 1/(1+Sqrt(5)))): n in [1..100]]; // G. C. Greubel, Nov 16 2018
(SageMath) [floor((3+sqrt(5))*(n - 1/(1+sqrt(5)))) for n in (1..100)] # G. C. Greubel, Nov 16 2018

Crossrefs

Cf. A184117, A184516.

Sequence in context: A179993 A252658 A140492 * A028252 A299647 A063617

Adjacent sequences: A184514 A184515 A184516 * A184518 A184519 A184520

Keyword

nonn

Author

Clark Kimberling, Jan 16 2011

Status

approved