A340016 Fixed points of A109812.

1, 2, 12, 14, 37, 199022, 365264, 12746116, 104351443

Offset: 1

Author

Thomas Scheuerle, Dec 26 2020

Keywords

• nonn
• more
• hard

Comments

The permutation A109812 has regions with smaller amplitude of A109812(n) - n in relative proximity to values of A305370 (Index of 2^n in A109812), this causes higher probability of fixed points in these regions.

The permutation A109812 has only weak selfsimilarity and increases its complexity with each interval 2^m..2^(m+1), by this increasing complexity it will be extremely difficult to find any rules and proofs regarding fixed points.

Links

• Thomas Scheuerle, MATLAB program for calculation of this sequence.
• Thomas Scheuerle, Graph of A109812(n) - n shows periodic regions of higher probability for fixed points.

Crossrefs

Cf. A109812.

Programs

MATLAB

See Thomas Scheuerle link.

Formula

A109812(a(n)) = a(n).

Extensions

a(8) from Chai Wah Wu, Jan 15 2021

a(9) from Walter Trump, Apr 13 2022