A283765 -id:A283765 - cp's OEIS frontend

A283766 Numbers k such that L(k) is odd, where L = A000201 = lower Wythoff sequence.

1, 2, 6, 7, 11, 12, 13, 16, 17, 18, 21, 22, 23, 27, 28, 32, 33, 34, 37, 38, 39, 42, 43, 44, 48, 49, 53, 54, 58, 59, 60, 63, 64, 65, 69, 70, 74, 75, 79, 80, 81, 84, 85, 86, 90, 91, 95, 96, 100, 101, 102, 105, 106, 107, 110, 111, 112, 116, 117, 121, 122, 123

Offset: 1

Clark Kimberling, Mar 17 2017

Complement of A283765.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A000201, A001622, A105774, A283765, A283768.

Cf. A085002 (characteristic function), A085003 (a left inverse).

r = GoldenRatio; z = 250; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 2];
Flatten[Position[u, 0]]  (* A283765 *)
Flatten[Position[u, 1]]  (* A283766 *)

a(n+1) - a(n) is in {1,3,4} for every n.

A085003(a(n)) = n for all n >= 1. - Antti Karttunen, Mar 17 2017

A283767 Numbers k such that U(k) is even, where U = A001950 = upper Wythoff sequence.

Original entry on oeis.org

1, 4, 7, 8, 10, 11, 13, 14, 17, 20, 21, 23, 24, 26, 27, 30, 33, 36, 37, 39, 40, 43, 46, 49, 50, 52, 53, 56, 59, 62, 63, 65, 66, 68, 69, 72, 75, 76, 78, 79, 81, 82, 85, 88, 91, 92, 94, 95, 98, 101, 104, 105, 107, 108, 111, 114, 117, 118, 120, 121, 123, 124

Offset: 1

Clark Kimberling, Mar 17 2017

Complement of A283768.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A001950, A001622, A283765, A283768.

r = GoldenRatio^2; z = 250; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 2];
Flatten[Position[u, 0]]  (* A283767 *)
Flatten[Position[u, 1]]  (* A283768 *)

a(n+1) - a(n) is in {1,2,3} for every n.

A283768 Numbers k such that U(k) is odd, where U = A001950 = upper Wythoff sequence.

Original entry on oeis.org

2, 3, 5, 6, 9, 12, 15, 16, 18, 19, 22, 25, 28, 29, 31, 32, 34, 35, 38, 41, 42, 44, 45, 47, 48, 51, 54, 55, 57, 58, 60, 61, 64, 67, 70, 71, 73, 74, 77, 80, 83, 84, 86, 87, 89, 90, 93, 96, 97, 99, 100, 102, 103, 106, 109, 110, 112, 113, 115, 116, 119, 122, 125

Offset: 1

Clark Kimberling, Mar 17 2017

Complement of A283767.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A001950, A001622, A283765, A283767.

r = GoldenRatio^2; z = 250; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 2];
Flatten[Position[u, 0]]  (* A283767 *)
Flatten[Position[u, 1]]  (* A283768 *)

a(n+1) - a(n) is in {1,2,3} for every n.

cp's OEIS Frontend

A283766 Numbers k such that L(k) is odd, where L = A000201 = lower Wythoff sequence.

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A283767 Numbers k such that U(k) is even, where U = A001950 = upper Wythoff sequence.

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A283768 Numbers k such that U(k) is odd, where U = A001950 = upper Wythoff sequence.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula