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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A205692 The number j such that 6 divides prime(k)-prime(j), where k(n)=A205691(n).

Original entry on oeis.org

3, 4, 3, 5, 4, 6, 3, 5, 7, 3, 5, 7, 9, 4, 6, 8, 4, 6, 8, 11, 3, 5, 7, 9, 10, 4, 6, 8, 11, 12, 3, 5, 7, 9, 10, 13, 3, 5, 7, 9, 10, 13, 15, 3, 5, 7, 9, 10, 13, 15, 16, 4, 6, 8, 11, 12, 14, 4, 6, 8, 11, 12, 14, 18, 3, 5, 7, 9, 10, 13, 15, 16, 17, 4, 6, 8, 11, 12, 14, 18
Offset: 1

Views

Author

Clark Kimberling, Jan 31 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205691.)

Crossrefs

Cf. A205691, A205558.

Programs

  • Mathematica
    (See the program at A205691.)

A205699 The number j such that 7 divides prime(k)-prime(j), where k(n)=A205698(n).

Original entry on oeis.org

2, 3, 1, 2, 7, 1, 9, 6, 10, 3, 8, 5, 2, 7, 11, 3, 8, 15, 5, 16, 10, 14, 2, 7, 11, 17, 1, 9, 12, 6, 13, 3, 8, 15, 18, 6, 13, 23, 2, 7, 11, 17, 21, 3, 8, 15, 18, 24, 1, 9, 12, 22, 5, 16, 19, 10, 14, 20, 10, 14, 20, 30, 3, 8, 15, 18, 24, 27, 5, 16, 19, 29, 6, 13, 23, 25, 1, 9
Offset: 1

Views

Author

Clark Kimberling, Jan 31 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205698.)

Crossrefs

Cf. A204890, A205698, A205558.

Programs

  • Mathematica
    (See the program at A205698.)

A205706 The number j such that 8 divides prime(k)-prime(j), where k(n)=A205705(n).

Original entry on oeis.org

2, 3, 2, 5, 4, 3, 6, 4, 9, 3, 6, 10, 7, 2, 5, 8, 4, 9, 11, 3, 6, 10, 12, 2, 5, 8, 14, 3, 6, 10, 12, 16, 2, 5, 8, 14, 17, 4, 9, 11, 15, 7, 13, 4, 9, 11, 15, 20, 2, 5, 8, 14, 17, 19, 7, 13, 21, 7, 13, 21, 24, 3, 6, 10, 12, 16, 18, 4, 9, 11
Offset: 1

Views

Author

Clark Kimberling, Jan 31 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205705.)

Crossrefs

Cf. A204890, A205705, A205558.

Programs

  • Mathematica
    (See the program at A205705.)

A205713 The number j such that 9 divides prime(k)-prime(j), where k(n)=A205712(n).

Original entry on oeis.org

1, 3, 1, 5, 6, 8, 3, 9, 4, 1, 5, 10, 7, 3, 9, 13, 4, 14, 6, 11, 7, 16, 8, 12, 4, 14, 18, 1, 5, 10, 15, 7, 16, 20, 4, 14, 18, 22, 1, 5, 10, 15, 23, 6, 11, 19, 7, 16, 20, 24, 8, 12, 21, 3, 9, 13, 17, 8, 12, 21, 29, 3, 9, 13, 17, 30, 1, 5, 10, 15
Offset: 1

Views

Author

Clark Kimberling, Jan 31 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205712.)

Crossrefs

Cf. A204890, A205712, A205558.

Programs

  • Mathematica
    (See the program at A205712.)

A205721 The number j such that 10 divides prime(k)-prime(j), where k(n)=A205720(n).

Original entry on oeis.org

2, 4, 2, 6, 8, 5, 4, 7, 5, 11, 2, 6, 9, 4, 7, 12, 2, 6, 9, 14, 8, 10, 5, 11, 13, 4, 7, 12, 15, 5, 11, 13, 18, 2, 6, 9, 14, 16, 8, 10, 17, 2, 6, 9, 14, 16, 21, 8, 10, 17, 22, 4, 7, 12, 15, 19, 5, 11, 13, 18, 20, 2, 6, 9, 14, 16, 21, 23, 4, 7
Offset: 1

Views

Author

Clark Kimberling, Jan 31 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205720.)

Crossrefs

Cf. A204890, A205720, A205558.

Programs

  • Mathematica
    (See the program at A205720.)

A205675 (prime(k)-prime(j))/3: (A205557)/3.

Original entry on oeis.org

1, 3, 2, 2, 5, 4, 2, 4, 2, 7, 6, 4, 2, 9, 8, 6, 4, 2, 8, 6, 4, 10, 8, 6, 2, 13, 12, 10, 8, 6, 4, 12, 10, 8, 4, 2, 15, 14, 12, 10, 8, 6, 2, 17, 16, 14, 12, 10, 8, 4, 2, 19, 18, 16, 14, 12, 10, 6, 4, 2, 18, 16, 14, 10, 8, 6, 20, 18, 16, 12, 10, 8, 2, 23, 22, 20, 18, 16, 14, 10
Offset: 1

Views

Author

Clark Kimberling, Jan 30 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205560.)

Crossrefs

Cf. A205674, A205559, A205560, A205558.

Programs

  • Mathematica
    (See the program at A205560.)

A205682 (prime(k)-prime(j))/4, where the pairs (k,j) are given by A205677 and A205678.

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 4, 3, 2, 5, 4, 3, 1, 6, 4, 3, 7, 6, 5, 3, 2, 8, 6, 5, 2, 9, 7, 6, 3, 1, 10, 9, 8, 6, 5, 3, 11, 10, 9, 7, 6, 4, 1, 12, 10, 9, 6, 4, 3, 14, 13, 12, 10, 9, 7, 4, 3, 14, 12, 11, 8, 6, 5, 2, 16, 15, 14, 12, 11, 9, 6, 5, 2, 17, 16, 15, 13, 12, 10, 7
Offset: 1

Views

Author

Clark Kimberling, Jan 30 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205677.)

Crossrefs

Cf. A205681, A205677, A205558.

Programs

  • Mathematica
    (See the program at A205677.)

A205837 Numbers k for which 2 divides s(k)-s(j) for some j

Original entry on oeis.org

3, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16
Offset: 1

Views

Author

Clark Kimberling, Feb 01 2012

Keywords

Comments

For a guide to related sequences, see A205840.

Examples

			The first six terms match these differences:
s(3)-s(1) = 3-1 = 2
s(4)-s(1) = 5-1 = 4
s(4)-s(3) = 5-3 = 2
s(5)-s(2) = 8-2 = 6
s(6)-s(1) = 13-1 = 12
s(6)-s(3) = 13-3 = 10

Crossrefs

Cf. A204892, A205840, A205558.

Programs

  • Mathematica
    s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
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 = 2; t = d[c]           (* A205556 *)
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}]     (* A205837 *)
Table[j[n], {n, 1, z2}]     (* A205838 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}](* A205839 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}](* A205840 *)

A205547 The number j such that 3 divides prime(k)-prime(j), where k(n)=A205560(n).

Original entry on oeis.org

1, 1, 3, 4, 1, 3, 5, 4, 6, 1, 3, 5, 7, 1, 3, 5, 7, 9, 4, 6, 8, 4, 6, 8, 11, 1, 3, 5, 7, 9, 10, 4, 6, 8, 11, 12, 1, 3, 5, 7, 9, 10, 13, 1, 3, 5, 7, 9, 10, 13, 15, 1, 3, 5, 7, 9, 10, 13, 15, 16, 4, 6, 8, 11, 12, 14, 4, 6, 8, 11, 12, 14, 18, 1, 3, 5, 7, 9, 10, 13
Offset: 1

Views

Author

Clark Kimberling, Jan 30 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205560.)

Crossrefs

Cf. A205559, A205560.

Programs

  • Mathematica
    (See the program at A205560.)

A205557 prime(k)-prime(j), where the pairs (k,j) are given by A205560 and A205547.

Original entry on oeis.org

3, 9, 6, 6, 15, 12, 6, 12, 6, 21, 18, 12, 6, 27, 24, 18, 12, 6, 24, 18, 12, 30, 24, 18, 6, 39, 36, 30, 24, 18, 12, 36, 30, 24, 12, 6, 45, 42, 36, 30, 24, 18, 6, 51, 48, 42, 36, 30, 24, 12, 6, 57, 54, 48, 42, 36, 30, 18, 12, 6, 54, 48, 42, 30, 24, 18, 60, 54, 48, 36
Offset: 1

Views

Author

Clark Kimberling, Jan 30 2012

Keywords

Comments

For a guide to related sequences, see A205558.

Examples

			(See the example at A205560.)

Crossrefs

Cf. A205558, A205560, A205675.

Programs

  • Mathematica
    (See the program at A205560.)
Previous Showing 11-20 of 58 results. Next

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