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

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

0,1

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.

Links

Table of n, a(n) for n=0..85.

Formula

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

Example

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

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]

Crossrefs

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

Sequence in context: A132826 A242724 A100123 * A153633 A118388 A213913

Adjacent sequences: A228037 A228038 A228039 * A228041 A228042 A228043

Keyword

nonn,cons,easy

Author

Clark Kimberling, Aug 05 2013

Status

approved