cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A184658 floor(nr+h), where r=(1+sqrt(5))/2, h=-1/3; complement of A184659.

Original entry on oeis.org

1, 2, 4, 6, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 36, 38, 40, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 57, 59, 61, 62, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114, 116, 117, 119, 121, 122, 124, 125, 127, 129, 130, 132, 133, 135, 137, 138, 140, 142, 143, 145, 146, 148, 150, 151, 153, 154, 156, 158, 159, 161, 163, 164, 166, 167, 169, 171, 172, 174, 176, 177, 179, 180, 182, 184, 185, 187, 188, 190, 192, 193
Offset: 1

Views

Author

Clark Kimberling, Jan 19 2011

Keywords

Crossrefs

Cf. A184659, A000201 (lower Wythoff sequence).

Programs

  • Mathematica
    r=(1+5^(1/2))/2; h=-1/3; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184658 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (* A184659 *)

Formula

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

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

Original entry on oeis.org

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, 221, 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

Views

Author

Clark Kimberling, Jan 20 2011

Keywords

Crossrefs

Cf. A184734, A184659.

Programs

  • Mathematica
    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 *)
With[{c=(3+Sqrt[5])/2},Table[Floor[c*n+1/3-c/3],{n,120}]] (* Harvey P. Dale, Nov 04 2024 *)

Formula

a(n)=floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=1/3.

A184733 a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4; complement of A184732.

Original entry on oeis.org

3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 44, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 78, 81, 84, 86, 89, 92, 94, 97, 99, 102, 105, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, 133, 136, 139, 141, 144, 147, 149, 152, 154, 157, 160, 162, 165, 167, 170, 173, 175, 178, 181, 183, 186, 188, 191, 194, 196, 199, 201, 204, 207, 209, 212, 215, 217, 220, 222, 225, 228, 230, 233, 236, 238, 241, 243, 246, 249, 251, 254, 256, 259, 262, 264, 267, 270, 272, 275, 277, 280, 283, 285, 288, 291, 293, 296, 298, 301, 304, 306, 309, 311, 314
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2011

Keywords

Links

Crossrefs

Cf. A184732, A184659.

Programs

  • Maple
    A184733 := proc(n)
        phi := (1+sqrt(5))/2 ;
        n+floor((n+1/4)*phi) ;
end proc:
seq(A184733(n),n=1..100) ; # R. J. Mathar, Sep 04 2016
  • Mathematica
    r=(1+sqrt(5))/2, h=-1/4; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184732 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (*A184733 *)

Formula

a(n) = floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4.
Showing 1-3 of 3 results.

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