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URL: https://oeis.org/A096363

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A096363
Length of repeating cycle of the final n digits in the Fibonacci sequence.
2
60, 300, 1500, 15000, 150000, 1500000, 15000000, 150000000, 1500000000, 15000000000, 150000000000, 1500000000000, 15000000000000, 150000000000000, 1500000000000000, 15000000000000000, 150000000000000000, 1500000000000000000, 15000000000000000000, 150000000000000000000
OFFSET
1,1
COMMENTS
Pisano periods pi(10^(n-1)).
LINKS
Daniel Lance Herrick, On the Periodicity of the Terminal Digits in the 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.
FORMULA
a(n) = A001175(A011557(n)).
From Elmo R. Oliveira, Mar 28 2026: (Start)
G.f.: 60*x*(1 - 5*x - 25*x^2)/(1 - 10*x).
E.g.f.: (3/2)*(exp(10*x) - 1) + 15*x*(3 + 5*x).
a(n) = 15*10^(n-1) for n > 2.
a(n) = 10*a(n-1) for n > 3.
a(n) = 5*A114307(n) = 3*A216099(n+1). (End)
MATHEMATICA
Join[{60, 300}, LinearRecurrence[{10}, {1500}, 14]] (* Ray Chandler, Aug 09 2015 *)
PROG
(Haskell)
a096363 = a001175 . (10 ^) -- Reinhard Zumkeller, Jan 16 2014
CROSSREFS
KEYWORD
base,nonn,easy,changed
AUTHOR
Lekraj Beedassy, Jun 30 2004
EXTENSIONS
More terms from Eric W. Weisstein, Jul 01 2004
STATUS
approved