A184521 -id:A184521 - cp's OEIS frontend

A184520 Lower s-Wythoff sequence, where s=5n+1. Complement of A184521.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142

Offset: 1

Clark Kimberling, Jan 16 2011

nonn

See A184117 for the definition of lower and upper s-Wythoff sequences.

Cf. A184117, A184521.

k = 5; r = -1; 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}]
Table[b[n], {n, 120}]

A184620 a(n) = floor(nr+h), where r=sqrt(2), h=1/4; complement of A184621.

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 78, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 95, 96, 97, 99, 100, 102, 103, 104, 106, 107, 109, 110, 111, 113, 114, 116, 117, 119, 120, 121, 123, 124, 126, 127, 128, 130, 131, 133, 134, 136, 137, 138, 140, 141, 143, 144, 145, 147, 148, 150, 151, 152, 154, 155, 157, 158, 160, 161, 162, 164, 165, 167, 168, 169

Offset: 1

Clark Kimberling, Jan 18 2011

nonn

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A184618, A184521.

[Floor(n*Sqrt(2) + 1/4): n in [1..120]]; // G. C. Greubel, Aug 18 2018

r=2^(1/2); h=1/4; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184620 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (* A184621 *)

vector(120, n, floor(n*sqrt(2) + 1/4)) \\ G. C. Greubel, Aug 18 2018

a(n) = floor(n*r+h), where r=sqrt(2), h=1/4.

cp's OEIS Frontend

A184520 Lower s-Wythoff sequence, where s=5n+1. Complement of A184521.

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A184620 a(n) = floor(nr+h), where r=sqrt(2), h=1/4; complement of A184621.

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