A096363 Length of repeating cycle of the final n digits in the Fibonacci sequence.

60, 300, 1500, 15000, 150000, 1500000, 15000000, 150000000, 1500000000, 15000000000, 150000000000, 1500000000000, 15000000000000, 150000000000000, 1500000000000000, 15000000000000000

Offset

1,1

Comments

Pisano periods pi(10^(n-1)).

Links

Table of n, a(n) for n=1..16.

Daniel Lance Herrick, On the Periodicity of the Terminal Digits in Fibonacci Sequences, The Fibonacci Quarterly, Vol. 11, No. 5, page 535.

Dov Jarden, On the Periodicity of the Last Digits of the Fibonacci Numbers, The Fibonacci Quarterly, Vol. 1, No. 4, page 21.

Ron Knott, The final digits

Eric Weisstein's World of Mathematics, Pisano Period

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

a(n) = A001175(A011557(n)).

Mathematica

Join[{60, 300}, LinearRecurrence[{10}, {1500}, 14]] (* Ray Chandler, Aug 09 2015 *)

Prog

(Haskell)
a096363 = a001175 . (10 ^)  -- Reinhard Zumkeller, Jan 16 2014

Crossrefs

Cf. A001175, A000045.

Sequence in context: A146750 A298045 A063497 * A033591 A133118 A211336

Adjacent sequences: A096360 A096361 A096362 * A096364 A096365 A096366

Keyword

base,nonn

Author

Lekraj Beedassy, Jun 30 2004

Extensions

More terms from Eric W. Weisstein, Jul 01 2004

Status

approved