A175562 The periodic part of the decimal expansion of 1/Fibonacci(n) with any initial zeros placed at the end of the cycle.

0, 0, 0, 3, 0, 0, 769230, 476190, 2941176470588235, 18, 11235955056179775280898876404494382022471910, 4

Offset

1,4

Comments

A curiosity: the first six digits (with the first digit zero) of a(11): {0,1,1,2,3,5} are the first six Fibonacci numbers!

The next term of this sequence contains 232 digits (decimal form of the periodic part of 1/233 = 0.0042918454935622317596566523605150214...7210300).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..22

Example

1/Fibonacci(7) = 1/13 = 0.0769230769230769230... and digit-cycle is 769230, so a(7)= 769230.

Mathematica

fc[n_] := Block[{q}, q = Last[First[RealDigits[1/Fibonacci[n]]]]; If[IntegerQ[q], q = {}]; FromDigits[q]]; Table[fc[n], {n, 40}] (* see the Mathematica program in A036275 *)

Crossrefs

Cf. A036275.

Sequence in context: A009133 A180515 A009138 * A319330 A291204 A331414

Adjacent sequences: A175559 A175560 A175561 * A175563 A175564 A175565

Keyword

nonn,base

Author

Michel Lagneau, Jul 02 2010

Extensions

Name and comment corrected by T. D. Noe, Jul 06 2010

Status

approved