A001179 Leonardo logarithm of n.

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, 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, 1, 2, 2, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

Are the powers of 5 (together with 2) the indices of records in this sequence? - Charles R Greathouse IV, Aug 11 2022

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.
• 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
• Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 73.
• John D. Fulton and William L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
• Beth H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related to the Fibonacci Numbers [Annotated and scanned copy]
• Wikipedia, Pisano period

Crossrefs

Cf. A001175, A235249.

Programs

Haskell

a001179 1 = 0
a001179 n = if p == n then ll (p `div` 24) 1 else a001179 p
            where p = a001175 n
                  ll x k = if x == 1 then k else ll (x `div` 5) (k + 1)
-- Reinhard Zumkeller, Jan 15 2014

Formula

A235249(n) = 24*5^(a(n)-1) for n > 1. - Reinhard Zumkeller, Jan 15 2014