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.

A228040 Decimal expansion of sum of reciprocals, row 2 of Wythoff array, W = A035513.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 05 2013

Keywords

Comments

Let c be the constant given by A079586, that is, the sum of reciprocals of the Fibonacci numbers F(k) for k>=1. The number c-1, the sum of reciprocals of row 1 of W, is known to be irrational (see A079586). Conjecture: the same is true for all the other rows of W.
Let h be the constant given at A153387 and s(n) the sum of reciprocals of numbers in row n of W. Then h < 1 + s(n)*floor(n*tau) < c. Thus, s(n) -> 0 as n -> oo.

Examples

			1/4 + 1/7 + 1/11 + ... = 0.629524839876312449535461795341...

Crossrefs

Cf. A035513, A079586, A093540, A228041, A228042, A228043.

Programs

  • Mathematica
    f[n_] := f[n] = Fibonacci[n]; g = GoldenRatio; w[n_, k_] := w[n, k] = f[k + 1]*Floor[n*g] + f[k]*(n - 1);
n = 2; Table[w[n, k], {n, 1, 5}, {k, 1, 5}]
r = N[Sum[1/w[n, k], {k, 1, 2000}], 120]
RealDigits[r, 10]

Formula

Equals A093540 - 4/3. - Amiram Eldar, May 22 2021

A228041 Decimal expansion of sum of reciprocals, row 3 of Wythoff array, W = A035513.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 05 2013

Keywords

Comments

Let c be the constant given by A079586, that is, the sum of reciprocals of the Fibonacci numbers F(k) for k>=1. The number c-1, the sum of reciprocals of row 1 of W, is known to be irrational (see A079586). Conjecture: the same is true for all the other rows of W.
Let h be the constant given at A153387 and s(n) the sum of reciprocals of numbers in row n of W. Then h < 1 + s(n)*floor(n*tau) < c. Thus, s(n) -> 0 as n -> oo.

Examples

			1/6 + 1/10 + 1/16 + ...  = 0.4299428331215887765860056514594635898444...

Crossrefs

Cf. A035513, A079586, A228040, A228042, A228043.

Programs

  • Mathematica
    f[n_] := f[n] = Fibonacci[n]; g = GoldenRatio; w[n_, k_] := w[n, k] = f[k + 1]*Floor[n*g] + f[k]*(n - 1);
n = 3; Table[w[n, k], {n, 1, 5}, {k, 1, 5}]
r = N[Sum[1/w[n, k], {k, 1, 2000}], 120]
RealDigits[r, 10]

Formula

Equals A079586/2 - 5/4. - Amiram Eldar, May 22 2021

A228042 Decimal expansion of sum of reciprocals, row 4 of Wythoff array, W = A035513.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 05 2013

Keywords

Comments

Let c be the constant given by A079586, that is, the sum of reciprocals of the Fibonacci numbers F(k) for k>=1. The number c-1, the sum of reciprocals of row 1 of W, is known to be irrational (see A079586). Conjecture: the same is true for all the other rows of W.
Let h be the constant given at A153387 and s(n) the sum of reciprocals of numbers in row n of W. Then h < 1 + s(n)*floor(n*tau) < c. Thus, s(n) -> 0 as n -> oo.

Examples

			1/9 + 1/15 + 1/24 + ... = 0.28662855541439251772400376763964239322963...

Crossrefs

Cf. A035513, A079586, A228040, A228041, A228043.

Programs

  • Mathematica
    f[n_] := f[n] = Fibonacci[n]; g = GoldenRatio; w[n_, k_] := w[n, k] = f[k + 1]*Floor[n*g] + f[k]*(n - 1);
n = 4; Table[w[n, k], {n, 1, 5}, {k, 1, 5}]
r = N[Sum[1/w[n, k], {k, 1, 2000}], 120]
RealDigits[r, 10]

Formula

Equals A079586/3 - 5/6. - Amiram Eldar, May 22 2021
Showing 1-3 of 3 results.

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