A184582 -id:A184582 - cp's OEIS frontend

A184583 floor[(n-1/5)(1+r)], where r=(1+sqrt(5))/2; complement of A184582.

2, 4, 7, 9, 12, 15, 17, 20, 23, 25, 28, 30, 33, 36, 38, 41, 43, 46, 49, 51, 54, 57, 59, 62, 64, 67, 70, 72, 75, 78, 80, 83, 85, 88, 91, 93, 96, 98, 101, 104, 106, 109, 112, 114, 117, 119, 122, 125, 127, 130, 132, 135, 138, 140, 143, 146, 148, 151, 153, 156, 159, 161, 164, 167, 169, 172, 174, 177, 180, 182, 185, 187, 190, 193, 195, 198, 201, 203, 206, 208, 211, 214, 216, 219, 222, 224, 227, 229, 232, 235, 237, 240, 242, 245, 248, 250, 253, 256, 258, 261, 263, 266, 269, 271, 274, 276, 279, 282, 284, 287, 290, 292, 295, 297, 300, 303, 305, 308, 311, 313

Offset: 1

Clark Kimberling, Jan 17 2011

nonn

Cf. A184582.

r=(1+5^(1/2))/2; c=-1/5; s=r/(r-1);
Table[Floor[n*r-c*r],{n,1,120}]  (* A184582 *)
Table[Floor[n*s+c*s],{n,1,120}]  (* A184583 *)

a(n)=floor[(n-1/5)(1+r)], where r=(1+sqrt(5))/2.

A184734 a(n)=floor(nr+h), where r=(1+sqrt(5))/2, h=1/3; complement of A184735.

Original entry on oeis.org

1, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 22, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 103, 105, 107, 108, 110, 111, 113, 115, 116, 118, 120, 121, 123, 124, 126, 128, 129, 131, 133, 134, 136, 137, 139, 141, 142, 144, 145, 147, 149, 150, 152, 154, 155, 157, 158, 160, 162, 163, 165, 166, 168, 170, 171, 173, 175, 176, 178, 179, 181, 183, 184, 186, 188, 189, 191, 192, 194

Offset: 1

Clark Kimberling, Jan 20 2011

nonn

Differs from A184582 first at index n=137. - R. J. Mathar, Jan 29 2011

Cf. A184735, A184658.

r=(1+sqrt(5))/2, h=1/3; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184734 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (*A184735 *)

a(n)=floor(nr+h), where r=(1+sqrt(5))/2, h=1/3.

A382116 a(n) = floor(n*g+(g-1)/2), where g is the golden ratio.

Original entry on oeis.org

0, 1, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 22, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 103, 105

Offset: 0

Jeffrey Shallit, Mar 16 2025

Differs from A184734(n) and A184582(n) at n = 27.

Consists of the values of A382113 in ascending order.

Cf. A001622, A382113.

Table[Floor[n*GoldenRatio+(GoldenRatio-1)/2],{n,0,65}] (* James C. McMahon, Mar 23 2025 *)

cp's OEIS Frontend

A184583 floor[(n-1/5)(1+r)], where r=(1+sqrt(5))/2; complement of A184582.

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Formula

A184734 a(n)=floor(nr+h), where r=(1+sqrt(5))/2, h=1/3; complement of A184735.

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Formula

A382116 a(n) = floor(n*g+(g-1)/2), where g is the golden ratio.

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