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A184517 Upper s-Wythoff sequence, where s=4n-2.  Complement of A184516. 2
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 (list; graph; refs; listen; history; text; internal format)
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

(Sage) [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

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Last modified December 18 18:37 EST 2018. Contains 318243 sequences. (Running on oeis4.)