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

1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 101, 102, 104, 105, 106, 107, 109, 110, 111, 112, 114, 115, 116, 117, 119, 120, 121, 122, 123, 125, 126, 127, 128, 130, 131, 132, 133, 135, 136, 137, 138, 140, 141, 142, 143, 145, 146, 147, 148

Offset

1,2

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.

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 *)

Prog

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

Crossrefs

Cf. A184117, A184517.

Sequence in context: A039243 A265187 A039186 * A184738 A032769 A039139

Adjacent sequences: A184513 A184514 A184515 * A184517 A184518 A184519

Keyword

nonn

Author

Clark Kimberling, Jan 16 2011

Status

approved