The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001178 Fibonacci frequency of n. (Formerly M3207 N1298) 3
 0, 4, 3, 2, 3, 1, 2, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 2, 2, 2, 2, 2, 0, 3, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 1, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 4, 1, 2, 2, 2, 3, 3, 1, 3, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(A235702(n)) = 0. - Reinhard Zumkeller, Jan 15 2014 a(n) is the least nonnegative integer k such that the function iterates f: {1, 2, ...} -> {1, 2, ...}, n -> f(n) = A001175(n), satisfy f^[k+1](n) = f^[k](n), where f^ is the identity map f^(n) = n and f^[k+1] = f o f^[k]. See the Fulton and Morris link, where the function f is called pi and a(n)= omega(n) for n >= 2, and omega(24) should be 0. (see the Zumkeller remark on the Hannon and Morris reference) - Wolfdieter Lang, Jan 18 2015 REFERENCES B. H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related to the Fibonacci Numbers. Report ORNL-4261, Oak Ridge National Laboratory, Oak Ridge, Tennessee, Jun 1968. [There is a typo in the value of a(24) given in the table on the last page.] N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110. B. H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related to the Fibonacci Numbers [Annotated and scanned copy] Wikipedia, Pisano period FORMULA See a comment above and the program. MATHEMATICA pi = 1; pi[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[ Fibonacci[k+1], n] == 1, Return[k]]]; a[n_] := Length[FixedPointList[pi, n]] - 2; a /@ Range (* Jean-François Alcover, Oct 28 2019 *) PROG (Haskell) a001178 = f 0 where    f j x = if x == y then j else f (j + 1) y  where y = a001175 x -- Reinhard Zumkeller, Jan 15 2014 CROSSREFS Cf. A001175, A235702. Sequence in context: A269611 A090342 A010307 * A016501 A248912 A152062 Adjacent sequences:  A001175 A001176 A001177 * A001179 A001180 A001181 KEYWORD nonn AUTHOR EXTENSIONS a(24) corrected by Reinhard Zumkeller, Jan 15 2014 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.

Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)