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A228042 Decimal expansion of sum of reciprocals, row 4 of Wythoff array, W = A035513. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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.

EXAMPLE

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

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]

CROSSREFS

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

Sequence in context: A206099 A021353 A131361 * A239386 A011370 A021890

Adjacent sequences:  A228039 A228040 A228041 * A228043 A228044 A228045

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Aug 05 2013

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)