login
Leonardo logarithm of n.
(Formerly M0052 N0017)
3

%I M0052 N0017 #32 Oct 22 2024 09:45:24

%S 0,1,1,1,2,1,1,1,1,2,2,1,1,1,2,1,1,1,1,2,1,2,1,1,3,1,1,1,1,2,2,1,2,1,

%T 2,1,1,1,1,2,2,1,2,2,2,1,1,1,1,3,1,1,1,1,2,1,1,1,1,2,2,2,1,1,2,2,1,1,

%U 1,2,2,1

%N Leonardo logarithm of n.

%C Are the powers of 5 (together with 2) the indices of records in this sequence? - _Charles R Greathouse IV_, Aug 11 2022

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Reinhard Zumkeller, <a href="/A001179/b001179.txt">Table of n, a(n) for n = 1..10000</a>

%H Nicholas John Bizzell-Browning, <a href="https://bura.brunel.ac.uk/handle/2438/29960">LIE scales: Composing with scales of linear intervallic expansion</a>, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 73.

%H John D. Fulton and William L. Morris, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1621.pdf">On arithmetical functions related to the Fibonacci numbers</a>, Acta Arithmetica, 16 (1969), 105-110.

%H Beth H. Hannon and W. L. Morris, <a href="/A001175/a001175.pdf">Tables of Arithmetical Functions Related to the Fibonacci Numbers</a> [Annotated and scanned copy]

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pisano_period">Pisano period</a>

%F A235249(n) = 24*5^(a(n)-1) for n > 1. - _Reinhard Zumkeller_, Jan 15 2014

%o (Haskell)

%o a001179 1 = 0

%o a001179 n = if p == n then ll (p `div` 24) 1 else a001179 p

%o where p = a001175 n

%o ll x k = if x == 1 then k else ll (x `div` 5) (k + 1)

%o -- _Reinhard Zumkeller_, Jan 15 2014

%Y Cf. A001175, A235249.

%K nonn,nice,changed

%O 1,5

%A _N. J. A. Sloane_