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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A205870 [s(k)-s(j)]/8, where the pairs (k,j) are given by A205867 and A205868, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

1, 2, 1, 4, 11, 17, 29, 18, 47, 36, 18, 76, 72, 123, 199, 198, 197, 322, 305, 522, 521, 520, 323, 845, 844, 843, 646, 323, 1368, 1364, 1292, 2207, 3582, 3571, 3553, 3535, 5795, 5778, 5473, 9378, 9367, 9349, 9331, 5796, 15174, 15163, 15145, 15127
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(6)-s(4) = 13-5 = 8 = 8*1
s(7)-s(4) = 21-5 = 16 = 8*2
s(7)-s(6) = 21-13 = 8 = 8*1
s(8)-s(2) = 34-2 = 32 = 8*4
s(10)-s(1) = 89-1 = 88 = 8*11
s(11)-s(5) = 144-8 = 136 =8*17

Crossrefs

Cf. A204892, A205867, A205869.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 8; t = d[c]    (* A205866 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]   (* A205867 *)
Table[j[n], {n, 1, z2}]     (* A205868 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205869 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205870 *)

A205874 s(k)-s(j), where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

18, 54, 81, 225, 144, 369, 288, 144, 576, 1584, 2583, 2529, 4176, 5778, 10944, 17703, 17622, 17478, 17334, 28656, 28602, 26073, 46224, 75024, 74970, 72441, 46368, 121392, 121338, 118809, 92736, 46368, 196416, 185472, 317808, 317790
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			(See the example at A205872.)

Crossrefs

Cf. A204890, A205872, A205840.

Programs

  • Mathematica
    (See the program at A205872.)

A205875 [s(k)-s(j)]/9, where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

2, 6, 9, 25, 16, 41, 32, 16, 64, 176, 287, 281, 464, 642, 1216, 1967, 1958, 1942, 1926, 3184, 3178, 2897, 5136, 8336, 8330, 8049, 5152, 13488, 13482, 13201, 10304, 5152, 21824, 20608, 35312, 35310, 57136, 56672, 92448, 92439, 92423, 92407
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(7)-s(3) = 21-3 = 18 = 9*2
s(9)-s(1) = 55-1 = 54 = 9*6
s(10)-s(5) = 89-8 = 81 = 9*9
s(12)-s(5) = 233-8 = 225 = 9*25
s(12)-s(10) = 233-89 = 144 = 9*16
s(13)-s(5) = 377-8 = 369 =9*41

Crossrefs

Cf. A204892, A205872, A205874.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 9; t = d[c]     (* A205871 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]       (* A205872 *)
Table[j[n], {n, 1, z2}]         (* A205873 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]   (* A205874 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205875 *)

A205879 s(k)-s(j), where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

10, 20, 50, 110, 230, 220, 610, 1220, 610, 2550, 2440, 4180, 4160, 6760, 6710, 17710, 17690, 13530, 28280, 27670, 27060, 46360, 75020, 74970, 68260, 121390, 121380, 121160, 196410, 150050, 317810, 317790, 313630, 300100, 514140
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			(See the example at A205877.)

Crossrefs

Cf. A204890, A205877, A205840.

Programs

  • Mathematica
    (See the program at A205877.)

A205880 [s(k)-s(j)]/10, where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.

Original entry on oeis.org

1, 2, 5, 11, 23, 22, 61, 122, 61, 255, 244, 418, 416, 676, 671, 1771, 1769, 1353, 2828, 2767, 2706, 4636, 7502, 7497, 6826, 12139, 12138, 12116, 19641, 15005, 31781, 31779, 31363, 30010, 51414, 83143, 134618, 83204, 217822, 166408, 83204
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first three terms match these differences:
s(6)-s(3) = 13-3 = 10 = 10*1
s(7)-s(1) = 21-1 = 20 = 10*2
s(9)-s(4) = 55-5 = 50 = 10*5

Crossrefs

Cf. A204892, A205877, A205879.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]  (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 10; t = d[c]    (* A205876 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]   (* A205877 *)
Table[j[n], {n, 1, z2}]   (* A205878 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205880 *)

A205556 Positions of multiples of 2 in A204922 (differences of Fibonacci numbers).

Original entry on oeis.org

2, 4, 6, 8, 11, 13, 14, 16, 18, 19, 21, 23, 26, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 47, 50, 53, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 76, 78, 80, 83, 86, 89, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106, 108, 109, 111, 112, 114, 115, 117
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			In A204922=(1,2,1,4,3,2,7,6,5,3,12,11,...), multiples of 2 are in positions 2,4,6,8,11,...  See the example at A205837.

Crossrefs

Cf. A204890, A205837, A205840.

Programs

  • Mathematica
    (See the program at A205837.)

A205839 s(k)-s(j), where the pairs (k,j) are given by A205837 and A205838.

Original entry on oeis.org

2, 4, 2, 6, 12, 10, 8, 20, 18, 16, 8, 32, 26, 54, 52, 50, 42, 34, 88, 86, 84, 76, 68, 34, 142, 136, 110, 232, 230, 228, 220, 212, 178, 144, 376, 374, 372, 364, 356, 322, 288, 144, 608, 602, 576, 466, 986, 984, 982, 974, 966, 932, 898, 754, 610, 1596
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			(See the example at A205587.)

Crossrefs

Cf. A204890, A205587, A205840.

Programs

  • Mathematica
    (See the program at A205587.)

A205841 Positions of multiples of 3 in A204922 (differences of Fibonacci numbers).

Original entry on oeis.org

5, 8, 10, 11, 18, 22, 27, 29, 34, 36, 38, 40, 41, 48, 52, 57, 59, 60, 65, 68, 70, 71, 76, 78, 79, 84, 86, 87, 94, 98, 102, 106, 111, 113, 114, 119, 121, 126, 128, 129, 134, 136, 138, 140, 141, 146, 148, 149, 156, 160, 164, 168, 173, 175, 176, 181, 183, 184
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			In A204922=(1,2,1,4,3,2,7,6,5,3,12,11,...), multiples of 3 are in positions 5,8,10,11,18,...  See the example at A205842.

Crossrefs

Cf. A204890, A205842, A205840.

Programs

  • Mathematica
    (See the program at A205842.)

A205846 Positions of multiples of 4 in A204922 (differences of Fibonacci numbers).

Original entry on oeis.org

4, 11, 14, 16, 19, 21, 23, 31, 37, 40, 42, 43, 50, 56, 59, 61, 62, 65, 67, 70, 72, 73, 76, 78, 80, 86, 94, 100, 106, 109, 111, 112, 115, 117, 118, 125, 131, 137, 140, 142, 143, 146, 148, 149, 152, 154, 157, 159, 160, 163, 165, 166, 169, 171, 173, 179
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			In A204922=(1,2,1,4,3,2,7,6,5,3,12,11,...), multiples of 4 are in positions 4,11,14,16,19,...  See the example at A205847.

Crossrefs

Cf. A204890, A205847, A205840.

Programs

  • Mathematica
    (See the program at A205847.)

A205851 Positions of multiples of 5 in A204922 (differences of Fibonacci numbers).

Original entry on oeis.org

9, 13, 15, 16, 32, 44, 53, 55, 58, 60, 61, 68, 82, 87, 93, 104, 107, 118, 120, 128, 130, 131, 137, 143, 157, 162, 167, 172, 178, 189, 191, 197, 208, 210, 212, 223, 225, 226, 234, 236, 237, 243, 257, 262, 267, 272, 279, 281, 282, 288, 299, 303, 305, 306
Offset: 1

Views

Author

Clark Kimberling, Feb 02 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			In A204922=(1,2,1,4,3,2,7,6,5,3,12,11,...), multiples
of 5 are in positions 9,13,15,16,32,... See the example
at A205852.

Crossrefs

Cf. A204890, A205852, A205840.

Programs

  • Mathematica
    (See the program at A205852.)
Previous Showing 31-40 of 44 results. Next

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