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

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, A184517.

Programs

Magma

[Floor((Sqrt(5)-1)*(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 *)

PARI

vector(100, n, floor((sqrt(5)-1)*(n + 1/(1+sqrt(5))))) \\ 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