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A184516 Lower s-Wythoff sequence, where s=4n-2.  Complement of A184517. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 15:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)