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

%I #54 May 02 2018 12:50:39

%S 1,3,7,15,27,703,1819,4255,4591,9663,26623,60975,77671,113383,159487,

%T 1212415,2684647,3041127,3873535,4637979,5656191,6416623,6631675,

%U 19638399,80049391,210964383,319804831,1410123943,70141259775,77566362559

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

%C 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

%C A proper subsequence of A006884. - _Robert G. Wilson v_, Dec 23 2017

%C 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

%H Howard A. Landman, <a href="/A025587/b025587.txt">Table of n, a(n) for n = 0..33</a> (a(0)-a(23) from _David W. Wilson_, a(24)-a(26) from Larry Reeves, a(27) from _Jud McCranie_)

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%t 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 *)

%o (C)

%o // First column is this sequence.

%o // Second column is the maximum (even) N reached.

%o // Third column is A061523, the ratio of those.

%o // NOTE: This could be made faster by special-casing 1,

%o // starting at 3, and incrementing by 4, since all terms except 1

%o // are congruent to 3 (mod 4).

%o #include <stdio.h>

%o long long i=1, n, max_n;

%o long double max_ratio=1.0, ratio;

%o int main()

%o {

%o while(1)

%o {

%o n = i;

%o max_n = n;

%o while (n > i) // Can stop as soon as we drop below start.

%o {

%o n = 3*n + 1;

%o max_n = (n > max_n) ? n : max_n;

%o while (!(n&1))

%o {

%o n >>= 1;

%o }

%o }

%o ratio = (double) max_n / (double) i;

%o if (ratio > max_ratio)

%o {

%o max_ratio = ratio;

%o printf("%lld\t%lld\t%Lf\n", i, max_n, max_ratio);

%o }

%o i += 2;

%o }

%o }

%o // _Howard A. Landman_, Nov 14 2017

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

%Y Cf. A006884, A070165.

%K nonn,nice

%O 0,2

%A _David W. Wilson_

%E More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001

%E a(27) from _Jud McCranie_, Apr 23 2012

%E a(26) corrected (was missing least significant digit) by _Howard A. Landman_, Nov 14 2017