

A306978


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


0



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
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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(n1) <= 3.  Daniel Suteu, Mar 20 2019


LINKS



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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



