OFFSET
0,2
COMMENTS
This sequence uses the highest even number reached, which will always be a power of 2 larger than A295163. - Howard A. Landman, Nov 20 2017
A proper subsequence of A006884. - Robert G. Wilson v, Dec 23 2017
Let m be the maximum value in row n of A070165. This sequence is the record transform of the sequence m/n for n >= 1. - Michael De Vlieger, Mar 13 2018
LINKS
Howard A. Landman, Table of n, a(n) for n = 0..33 (a(0)-a(23) from David W. Wilson, a(24)-a(26) from Larry Reeves, a(27) from Jud McCranie)
MATHEMATICA
With[{s = Array[Max@ NestWhileList[If[EvenQ@#, #/2, 3 # + 1] &, #, # > 1 &]/# &, 2^18]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Mar 13 2018 *)
PROG
(C)
// First column is this sequence.
// Second column is the maximum (even) N reached.
// Third column is A061523, the ratio of those.
// NOTE: This could be made faster by special-casing 1,
// starting at 3, and incrementing by 4, since all terms except 1
// are congruent to 3 (mod 4).
#include <stdio.h>
long long i=1, n, max_n;
long double max_ratio=1.0, ratio;
int main()
{
while(1)
{
n = i;
max_n = n;
while (n > i) // Can stop as soon as we drop below start.
{
n = 3*n + 1;
max_n = (n > max_n) ? n : max_n;
while (!(n&1))
{
n >>= 1;
}
}
ratio = (double) max_n / (double) i;
if (ratio > max_ratio)
{
max_ratio = ratio;
printf("%lld\t%lld\t%Lf\n", i, max_n, max_ratio);
}
i += 2;
}
}
// Howard A. Landman, Nov 14 2017
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001
a(27) from Jud McCranie, Apr 23 2012
a(26) corrected (was missing least significant digit) by Howard A. Landman, Nov 14 2017
STATUS
approved