A306978 Numbers with record number of iterations of x -> A306938(x) required to reach 1 (A306944).

1, 2, 4, 7, 21, 49, 85, 253, 442, 766, 1327, 2299, 3982, 11839, 20506, 35518, 61519, 184557, 553645, 966928, 1674769, 2900785, 8701141, 25877593, 44821306, 77676682, 134539960, 402368674, 696922987, 1207106023, 2090768962, 3632578906

Offset

1,2

Comments

The record numbers of iterations are 0, 2, 4, 6, 7, 8, 10, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 29, 30, 32, 34, 36, 37, 38, 40, 42, 44, 45, 47, 49, 51, 53.

Conjecture: sqrt(3) < a(n)/a(n-1) <= 3. - Daniel Suteu, Mar 20 2019

Links

Table of n, a(n) for n=1..32.

H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example III.3.

Example

2 reaches 1 after 2 iterations: 2 -> 3 -> 1;
4 reaches 1 after a record number of 4 iterations: 4 -> 6 -> 2 -> 3 -> 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]; s={}; im=-1; Do[i=itnum[n]; If[i>im, im=i; AppendTo[s, n]], {n, 1, 10000}]; s

Crossrefs

Cf. A306938, A306943, A306944.

Sequence in context: A145777 A188497 A237759 * A337062 A153550 A102984

Adjacent sequences: A306975 A306976 A306977 * A306979 A306980 A306981

Keyword

nonn,more

Author

Amiram Eldar, Mar 18 2019

Status

approved