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.

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A184483 Upper s-Wythoff sequence, where s(n)=3n-1. Complement of A184482.

Original entry on oeis.org

3, 7, 12, 16, 20, 25, 29, 33, 37, 42, 46, 50, 55, 59, 63, 68, 72, 76, 80, 85, 89, 93, 98, 102, 106, 111, 115, 119, 124, 128, 132, 136, 141, 145, 149, 154, 158, 162, 167, 171, 175, 179, 184, 188, 192, 197, 201, 205, 210, 214, 218, 222, 227, 231, 235, 240, 244
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2011

Keywords

Crossrefs

Cf. A184117, A184482.

A184484 Lower s-Wythoff sequence, where s(n)=3n-2. Complement of A184485.

Original entry on oeis.org

1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 92, 94, 95, 96, 98, 99, 100, 102, 103, 104, 105, 107, 108, 109, 111, 112, 113, 115, 116, 117, 119, 120, 121, 122, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 137, 138, 139, 141, 142, 143, 145, 146, 147, 148, 150, 151, 152, 154, 155, 156
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2011

Keywords

Crossrefs

Cf. A184117, A184485.

Programs

  • Mathematica
    k=3; 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}]
Table[b[n],{n,120}]

A184485 Upper s-Wythoff sequence, where s(n)=3n-2. Complement of A184484.

Original entry on oeis.org

2, 7, 11, 15, 19, 24, 28, 32, 37, 41, 45, 50, 54, 58, 63, 67, 71, 75, 80, 84, 88, 93, 97, 101, 106, 110, 114, 118, 123, 127, 131, 136, 140, 144, 149, 153, 157, 161, 166, 170, 174, 179, 183, 187, 192, 196, 200, 204, 209, 213, 217, 222, 226, 230, 235, 239, 243
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2011

Keywords

Crossrefs

Cf. A184117, A184484.

A184516 Lower s-Wythoff sequence, where s=4n-2. Complement of A184517.

Original entry on oeis.org

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
Offset: 1

Views

Author

Clark Kimberling, Jan 16 2011

Keywords

Comments

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

Links

Crossrefs

Cf. A184117, A184517.

Programs

  • Magma
    [Floor((Sqrt(5)-1)*(n + 1/(1+Sqrt(5)))): n in [1..100]]; // G. C. Greubel, Nov 16 2018
  • 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 *)
  • PARI
    vector(100, n, floor((sqrt(5)-1)*(n + 1/(1+sqrt(5))))) \\ 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

A184522 Upper s-Wythoff sequence, where s=5n. Complement of A184523.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 143
Offset: 1

Views

Author

Clark Kimberling, Jan 16 2011

Keywords

Comments

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

Crossrefs

Cf. A184117, A184523.

Programs

  • Mathematica
    k = 5; r = 0; 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}]

Formula

a(n) = floor((n/2)*(-3+sqrt(29))).

A184420 Upper s-Wythoff sequence, where s=upper Wythoff sequence. Complement of A184419.

Original entry on oeis.org

2, 6, 8, 11, 15, 18, 21, 24, 27, 30, 33, 36, 40, 42, 46, 48, 52, 55, 58, 61, 64, 67, 71, 73, 77, 80, 82, 86, 89, 92, 95, 98, 102, 105, 107, 111, 113, 117, 120, 123, 126, 129, 132, 136, 138, 142, 145, 147, 151, 154, 157, 160, 163, 166, 169, 173, 176, 178, 182, 185, 188, 191, 194, 197, 201, 203, 207, 210, 212, 216, 218, 222, 226, 228, 231, 234, 238, 241, 243, 247, 250, 253, 256, 259, 262, 266, 268, 272, 275, 278, 281, 283, 287, 291, 293, 296, 299, 302, 306, 309
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2011

Keywords

Comments

See A184419.

Crossrefs

Cf. A184117, A184419.

Programs

  • Mathematica
    mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
r=(1+5^(1/2))/2;s[n_]:=Floor[r*n];a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,40}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]

A184421 Lower s-Wythoff sequence, where s=upper Wythoff sequence. Complement of A184422.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 67, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 92, 93, 95, 96, 97, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 112, 114, 115, 116, 117, 119, 120, 121, 123, 124, 125, 127, 128, 129, 131, 132, 133
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2011

Keywords

Comments

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

Crossrefs

Cf. A184117, A184422.

Programs

  • Mathematica
    mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
r=(1+5^(1/2))/2;s[n_]:=Floor[r*n+n];a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,40}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]

A184422 Upper s-Wythoff sequence, where s=upper Wythoff sequence. Complement of A184421.

Original entry on oeis.org

3, 7, 11, 15, 19, 23, 27, 30, 35, 39, 42, 47, 51, 54, 59, 62, 66, 71, 74, 78, 82, 86, 91, 94, 98, 102, 106, 110, 113, 118, 122, 126, 130, 134, 137, 142, 145, 149, 154, 157, 162, 165, 169, 173, 177, 181, 186, 189, 193, 197, 201, 205, 208, 213, 216, 221, 225, 228, 233, 237, 240, 245, 248, 252, 257, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 299, 304, 308, 311, 316, 320, 323, 328, 331, 336, 340, 343, 347, 352, 355, 359, 363, 367, 371, 375, 379, 382, 387, 391, 394
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2011

Keywords

Comments

See A184421.

Crossrefs

Cf. A184117, A184421.

Programs

  • Mathematica
    mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
r=(1+5^(1/2))/2;s[n_]:=Floor[r*n+n];a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,40}]
Table[a[n],{n,100}]
Table[b[n],{n,100}]

A184425 Lower s-Wythoff sequence, where s=A000217 (triangular numbers). Complement of A184426.

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2011

Keywords

Comments

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

Crossrefs

Cf. A184117, A184426.

Programs

  • Mathematica
    mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
s[n_]:=n (n+1)/2;a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,40}]
Table[a[n],{n,120}]
Table[b[n],{n,100}]

A184426 Upper s-Wythoff sequence, where s=A000217 (triangular numbers). Complement of A184425.

Original entry on oeis.org

2, 6, 10, 15, 22, 29, 37, 47, 57, 68, 80, 94, 108, 123, 139, 156, 174, 194, 214, 235, 257, 280, 304, 330, 356, 383, 411, 440, 470, 501, 534, 567, 601, 636, 672, 709, 747, 786, 826, 868, 910, 953, 997, 1042, 1088, 1135, 1183, 1232, 1283, 1334, 1386, 1439, 1493, 1548, 1604, 1661, 1719, 1778, 1839, 1900, 1962, 2025, 2089, 2154, 2220, 2287, 2355, 2424, 2494, 2566, 2638, 2711, 2785, 2860, 2936, 3013, 3091, 3170, 3250, 3331, 3413, 3496, 3581, 3666
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2011

Keywords

Comments

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

Crossrefs

Cf. A184117, A184425.

Programs

  • Mathematica
    mex:=First[Complement[Range[1,Max[#1]+1],#1]]&;
s[n_]:=n (n+1)/2;a[1]=1;b[n_]:=b[n]=s[n]+a[n];
a[n_]:=a[n]=mex[Flatten[Table[{a[i],b[i]},{i,1,n-1}]]];
Table[s[n],{n,40}]
Table[a[n],{n,120}]
Table[b[n],{n,100}]
Previous Showing 21-30 of 53 results. Next

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