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A306944
a(n) = number of iterations of x -> A306938(x) required to reach 1 when started at n, or -1 if the trajectory of n never reaches 1.
5
0, 2, 1, 4, -1, 3, 6, -1, 2, -1, -1, 5, -1, -1, -1, 4, -1, 4, -1, -1, 7, -1, -1, -1, -1, -1, 3, 6, -1, -1, -1, -1, -1, -1, -1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 5, 8, -1, -1, -1, -1, 5, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1
OFFSET
1,2
COMMENTS
If the trajectory of n contains two consecutive non-multiples of 3 then it increases for ever [te Riele].
LINKS
H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example III.3.
MATHEMATICA
f[n_] := If[Divisible[n, 3], n/3, Floor[n*Sqrt[3]]]; a[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]; Array[a, 100]; (* Amiram Eldar, Mar 17 2019 *)
CROSSREFS
Sequence in context: A239451 A216223 A078072 * A049776 A286235 A180339
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Mar 17 2019
EXTENSIONS
More terms from Amiram Eldar, Mar 17 2019
STATUS
approved