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

Author

Michael De Vlieger, Dec 30 2024

Keywords

• nonn
• tabf

Comments

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

Examples

			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;
  ...
		

Links

• 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

Crossrefs

Cf. A001175, A001179, A235249, A235702.

Programs

Mathematica

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}]