A306971 The number of initial values <= 10^n whose trajectory under the iteration x -> A306938(x) reaches 1.

7, 23, 63, 175, 459, 1349, 3506, 8820, 21897

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 number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. 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: A333187 A220509 A003261 * A343519 A365439 A266801

Adjacent sequences: A306968 A306969 A306970 * A306972 A306973 A306974

Keyword

nonn,more

Author

Amiram Eldar, Mar 18 2019

Status

approved