login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228041 Decimal expansion of sum of reciprocals, row 3 of Wythoff array, W = A035513. 4
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 (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

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

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]

CROSSREFS

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

Sequence in context: A097664 A144811 A185654 * A242049 A179398 A233295

Adjacent sequences:  A228038 A228039 A228040 * A228042 A228043 A228044

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Aug 05 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 13 21:28 EST 2019. Contains 329106 sequences. (Running on oeis4.)