

A306971


The number of initial values <= 10^n whose trajectory under the iteration x > A306938(x) reaches 1.


0




OFFSET

1,1


COMMENTS

te Riele noted that of the first initial values <= 10^5 only 459 have a trajectory that reaches 1 and conjectured that almost all trajectories tend to infinity.


LINKS

Table of n, a(n) for n=1..9.
H. J. J. te Riele, Iteration of numbertheoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345360. See Example III.3.


EXAMPLE

a(1) = 7 since 7 of the initial values 1 to 10 (all except 5, 8, and 10) have a trajectory that reaches 1 (their A306944 value is not 1).


MATHEMATICA

f[n_] := If[Divisible[n, 3], n/3, Floor[n*Sqrt[3]]]; itnum[n_] := Module[{k = n, inc = False, c = 0}, While[k > 1, kk = f[k]; If[inc && kk > k, c = 1; Break[]]; inc = kk > k; k = kk; c++]; c]; p=10; s={}; c=0; Do[i=itnum[n]; If[i>1, c++]; If[n==p, AppendTo[s, c]; p*=10], {n, 1, 10000}]; s


CROSSREFS

Cf. A306938, A306943, A306944.
Sequence in context: A201110 A220509 A003261 * A266801 A066187 A259214
Adjacent sequences: A306968 A306969 A306970 * A306972 A306973 A306974


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Mar 18 2019


STATUS

approved



