A295163 -id:A295163 - cp's OEIS frontend

A025587 '3x+1' record-setters (blowup factor).

1, 3, 7, 15, 27, 703, 1819, 4255, 4591, 9663, 26623, 60975, 77671, 113383, 159487, 1212415, 2684647, 3041127, 3873535, 4637979, 5656191, 6416623, 6631675, 19638399, 80049391, 210964383, 319804831, 1410123943, 70141259775, 77566362559

Offset: 0

David W. Wilson

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

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_)
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A295163 for maximum odd number reached, and A061523 for blowup factors.

Cf. A006884, A070165.

// 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    
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

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 *)

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

A061523 Integer part of the blowup factor for A025587(n).

Original entry on oeis.org

1, 5, 7, 10, 341, 356, 701, 1600, 1776, 2806, 3994, 9729, 20224, 21891, 107860, 115180, 131346, 204765, 221646, 284348, 426522, 748056, 9099150, 15596837, 27297444, 30359613, 4422186001

Offset: 0

Larry Reeves (larryr(AT)acm.org), May 03 2001

nonn

			a(4)=10 since A025587(4)=15 and starting with 15 in the Collatz sequence gives a maximum value of 160 with a blowup factor of 160/15 = 10.66666...

Cf. A025587, A295163.

With[{s = Array[Max@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 1 &]/# &, 2^18]}, Floor@ Union@ FoldList[Max, s]] (* Michael De Vlieger, Mar 13 2018 *)

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A025587 '3x+1' record-setters (blowup factor).

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