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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A265298 Decimal expansion of sum{c(2n) - x, n=1,2,...}, where c = convergents to (x = sqrt(5)).

Original entry on oeis.org

0, 1, 3, 9, 7, 5, 2, 9, 0, 4, 8, 4, 1, 6, 0, 6, 9, 4, 6, 3, 0, 4, 3, 1, 9, 3, 7, 0, 2, 8, 4, 6, 9, 2, 8, 1, 3, 5, 3, 8, 0, 0, 2, 5, 5, 6, 4, 1, 8, 4, 2, 4, 2, 7, 3, 4, 1, 7, 9, 8, 4, 7, 0, 7, 1, 5, 1, 8, 7, 0, 8, 2, 4, 8, 3, 8, 8, 2, 4, 0, 8, 6, 3, 3, 5, 8
Offset: 0

Views

Author

Clark Kimberling, Dec 07 2015

Keywords

Examples

			sum = 0.01397529048416069463043193702846928135380025564...

Crossrefs

Cf. A002163, A265297, A265299, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[5]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265297 *)
RealDigits[s2, 10, 120][[1]]  (* A265298 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)

A265299 Decimal expansion of sum{c(2n) - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)).

Original entry on oeis.org

2, 5, 0, 8, 1, 9, 5, 3, 9, 0, 5, 4, 3, 0, 8, 8, 8, 2, 2, 2, 5, 8, 1, 2, 1, 1, 5, 2, 5, 8, 3, 7, 0, 4, 7, 6, 1, 1, 4, 7, 8, 0, 6, 7, 5, 8, 2, 4, 5, 8, 8, 7, 8, 0, 8, 0, 7, 0, 3, 1, 8, 0, 1, 6, 1, 2, 1, 0, 5, 9, 5, 6, 9, 1, 4, 2, 4, 6, 2, 2, 9, 0, 8, 4, 6, 5
Offset: 0

Views

Author

Clark Kimberling, Dec 07 2015

Keywords

Examples

			sum = 0.25081953905430888222581211525837047611...

Crossrefs

Cf. A002163, A265297, A265298, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[5]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265297 *)
RealDigits[s2, 10, 120][[1]]  (* A265298 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)

A265300 Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(6)).

Original entry on oeis.org

4, 5, 4, 5, 8, 7, 1, 1, 3, 0, 6, 5, 0, 7, 2, 4, 7, 4, 9, 9, 8, 9, 7, 8, 3, 3, 0, 8, 0, 9, 5, 4, 3, 0, 1, 3, 3, 2, 5, 0, 8, 5, 3, 9, 7, 8, 3, 5, 3, 3, 9, 5, 4, 2, 6, 8, 1, 3, 8, 8, 7, 2, 6, 3, 3, 6, 6, 4, 0, 3, 9, 0, 4, 6, 5, 0, 4, 3, 5, 4, 0, 9, 4, 4, 5, 5
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.454587113065072474998978330809543013325085397...

Crossrefs

Cf. A010464, A265301, A265302, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[6]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265300 *)
RealDigits[s2, 10, 120][[1]]  (* A265301 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)

A265301 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(6)).

Original entry on oeis.org

5, 1, 0, 2, 5, 7, 7, 4, 8, 2, 8, 4, 4, 7, 5, 3, 6, 6, 8, 7, 0, 9, 7, 4, 1, 8, 6, 1, 6, 4, 1, 0, 1, 0, 5, 9, 5, 6, 1, 6, 0, 0, 2, 0, 2, 9, 8, 4, 0, 3, 7, 1, 6, 6, 0, 9, 9, 6, 8, 0, 9, 4, 1, 3, 0, 5, 2, 4, 6, 3, 3, 9, 0, 6, 3, 0, 8, 4, 9, 6, 2, 8, 1, 7, 3, 5
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.0510257748284475366870974186164101059561600202984037166...

Crossrefs

Cf. A010464, A265300, A265302, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[6]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265300 *)
RealDigits[s2, 10, 120][[1]]  (* A265301 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)

A265302 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(6).

Original entry on oeis.org

5, 0, 5, 6, 1, 2, 8, 8, 7, 8, 9, 3, 5, 2, 0, 0, 1, 1, 6, 8, 6, 0, 7, 5, 7, 4, 9, 4, 2, 5, 9, 5, 3, 1, 1, 9, 2, 8, 1, 2, 4, 5, 4, 1, 8, 1, 3, 3, 7, 4, 3, 2, 5, 9, 2, 9, 1, 3, 5, 6, 8, 2, 0, 4, 6, 7, 1, 6, 5, 0, 2, 4, 3, 7, 1, 3, 5, 2, 0, 3, 7, 2, 2, 6, 2, 9
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.50561288789352001168607574942595311928124541813374...

Crossrefs

Cf. A010464, A265300, A265301, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[6]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265300 *)
RealDigits[s2, 10, 120][[1]]  (* A265301 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)

A265303 Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).

Original entry on oeis.org

8, 5, 7, 7, 2, 0, 6, 7, 6, 1, 3, 6, 1, 9, 1, 9, 6, 6, 0, 0, 4, 2, 2, 2, 7, 3, 5, 2, 2, 6, 5, 4, 4, 6, 1, 4, 4, 7, 9, 2, 0, 3, 5, 3, 0, 2, 5, 1, 2, 1, 6, 5, 4, 9, 3, 3, 6, 6, 0, 5, 9, 2, 0, 4, 4, 6, 1, 1, 3, 8, 6, 2, 7, 4, 1, 3, 3, 0, 7, 1, 7, 6, 5, 2, 2, 8
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.8577206761361919660042227352265446144...

Crossrefs

Cf. A010466, A265304, A265305, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[8]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265303 *)
RealDigits[s2, 10, 120][[1]]  (* A265304 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)

A265304 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(8)).

Original entry on oeis.org

1, 7, 6, 6, 2, 7, 7, 6, 4, 3, 0, 5, 1, 5, 1, 8, 0, 6, 4, 3, 5, 7, 0, 5, 9, 6, 9, 4, 5, 0, 7, 9, 3, 8, 5, 7, 7, 3, 1, 8, 3, 9, 1, 8, 4, 4, 4, 8, 7, 2, 5, 5, 5, 7, 7, 5, 7, 7, 7, 7, 4, 0, 7, 0, 2, 8, 2, 6, 5, 8, 5, 4, 9, 0, 5, 2, 7, 5, 4, 5, 2, 9, 4, 0, 8, 7
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.176627764305151806435705969450793857731839184448725557757777...

Crossrefs

Cf. A010466, A265303, A265305, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[8]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265303 *)
RealDigits[s2, 10, 120][[1]]  (* A265304 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)

A265305 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(8).

Original entry on oeis.org

1, 0, 3, 4, 3, 4, 8, 4, 4, 0, 4, 4, 1, 3, 4, 3, 7, 7, 2, 4, 3, 9, 9, 2, 8, 7, 0, 4, 6, 7, 7, 3, 3, 8, 4, 7, 2, 2, 1, 1, 0, 4, 2, 7, 1, 4, 6, 9, 9, 9, 4, 2, 1, 0, 7, 0, 9, 4, 3, 8, 3, 3, 2, 7, 4, 7, 4, 3, 7, 9, 7, 1, 7, 6, 4, 6, 6, 0, 6, 1, 7, 0, 5, 9, 3, 1
Offset: 1

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 1.0343484404413437724399287046773384722110427146999...

Crossrefs

Cf. A010466, A265303, A265304, A265288 (guide).

Programs

  • Mathematica
    x = Sqrt[8]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265303 *)
RealDigits[s2, 10, 120][[1]]  (* A265304 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)

A265306 Decimal expansion of Sum_{k>=1} (e-c(2k-1)), where c = convergents to e.

Original entry on oeis.org

7, 7, 4, 2, 2, 8, 5, 8, 9, 2, 0, 8, 2, 1, 9, 6, 2, 0, 5, 5, 2, 9, 3, 3, 9, 6, 8, 9, 4, 0, 5, 9, 3, 6, 3, 8, 3, 7, 2, 4, 3, 7, 6, 3, 7, 2, 4, 2, 9, 7, 3, 9, 1, 6, 2, 1, 6, 1, 3, 2, 5, 9, 4, 2, 0, 3, 4, 3, 2, 8, 6, 6, 9, 8, 6, 7, 5, 3, 2, 4, 8, 4, 0, 8, 6, 3
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.77422858920821962055293396894059363837243763724297...

Crossrefs

Cf. A001113, A265306, A265307, A265288 (guide).

Programs

  • Mathematica
    x = E; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265306 *)
RealDigits[s2, 10, 120][[1]]  (* A265307 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)

A265307 Decimal expansion of Sum_{k>=1} (c(2k)-e), where c = convergents to e.

Original entry on oeis.org

3, 1, 3, 9, 3, 4, 3, 0, 5, 9, 8, 4, 4, 1, 2, 4, 0, 5, 2, 5, 6, 5, 9, 6, 0, 0, 7, 5, 9, 6, 8, 3, 4, 7, 7, 7, 8, 0, 0, 5, 7, 7, 7, 4, 9, 1, 4, 9, 6, 7, 1, 5, 1, 9, 5, 1, 3, 3, 1, 0, 1, 9, 7, 5, 8, 6, 6, 3, 8, 0, 2, 9, 1, 0, 5, 2, 2, 5, 2, 8, 5, 1, 6, 4, 1, 5
Offset: 0

Views

Author

Clark Kimberling, Dec 13 2015

Keywords

Examples

			sum = 0.3139343059844124052565960075968347778005777...

Crossrefs

Cf. A001113, A265306, A265308, A265288 (guide).

Programs

  • Mathematica
    x = E; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265306 *)
RealDigits[s2, 10, 120][[1]]  (* A265307 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265308 *)
Previous Showing 11-20 of 23 results. Next

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