A340016 Fixed points of A109812.

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

Offset

1,2

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

Table of n, a(n) for n=1..9.

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.

Formula

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

Prog

(MATLAB) See Thomas Scheuerle link.

Crossrefs

Cf. A109812.

Sequence in context: A259128 A280942 A270119 * A260899 A108969 A269130

Adjacent sequences: A340013 A340014 A340015 * A340017 A340018 A340019

Keyword

nonn,more,hard

Author

Thomas Scheuerle, Dec 26 2020

Extensions

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

a(9) from Walter Trump, Apr 13 2022

Status

approved