A235249 -id:A235249 - cp's OEIS frontend

A379646 Irregular triangle T(n,k) where row n contains the trajectory of recursive mappings of A001175(x) starting with x = n and ending at fixed point A235249(n).

1, 2, 3, 8, 12, 24, 3, 8, 12, 24, 4, 6, 24, 5, 20, 60, 120, 6, 24, 7, 16, 24, 8, 12, 24, 9, 24, 10, 60, 120, 11, 10, 60, 120, 12, 24, 13, 28, 48, 24, 14, 48, 24, 15, 40, 60, 120, 16, 24, 17, 36, 24, 18, 24, 19, 18, 24, 20, 60, 120, 21, 16, 24, 22, 30, 120, 23, 48, 24

Offset: 1

Michael De Vlieger, Dec 30 2024

Row n contains recursive mappings of A001175(x) starting with x = n.

			Table begins:
   1;
   2,  3,   8,  12, 24;
   3,  8,  12,  24;
   4,  6,  24;
   5, 20,  60, 120;
   6, 24;
   7, 16,  24;
   8, 12,  24;
   9, 24;
  10, 60, 120;
  11, 10,  60, 120;
  12, 24;
  ...

Michael De Vlieger, Table of n, a(n) for n = 1..10141 (rows n = 1..2500, flattened)
Brennan Benfield and Oliver Lippard, Fixed points of K-Fibonacci sequences, arXiv:2404.08194 [math.NT], 2024.
J. D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
Wikipedia, Pisano period

Cf. A001175, A001179, A235249, A235702.

q[{0, 1, }] := False; q[] := True;
f[k_][{a_, b_, c_}] := {Mod[b, k], Mod[a + b, k], c + 1};
s[1] := 1; s[k_] := s[k] = Which[
  PrimeQ[k] && k > 5, If[
    AnyTrue[PrimitiveRootList[k], Mod[#^2, k] == Mod[# + 1, k] &],
    k - 1,
    NestWhile[f[k], {1, 1, 1}, q][[-1]] ],
  PrimePowerQ[k], NestWhile[f[k], {1, 1, 1}, q][[-1]], True,
    LCM @@ Map[s[#] &, Power @@@ FactorInteger[k] ] ];
Table[Most@ FixedPointList[s[#] &, n], {n, 24}]

A001179 Leonardo logarithm of n.

Original entry on oeis.org

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

N. J. A. Sloane

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

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).

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

Cf. A001175, A235249.

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

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

cp's OEIS Frontend

A379646 Irregular triangle T(n,k) where row n contains the trajectory of recursive mappings of A001175(x) starting with x = n and ending at fixed point A235249(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica