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

%I A025587 #54 May 02 2018 12:50:39
%S A025587 1,3,7,15,27,703,1819,4255,4591,9663,26623,60975,77671,113383,159487,
%T A025587 1212415,2684647,3041127,3873535,4637979,5656191,6416623,6631675,
%U A025587 19638399,80049391,210964383,319804831,1410123943,70141259775,77566362559
%N A025587 '3x+1' record-setters (blowup factor).
%C A025587 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 A025587 A proper subsequence of A006884. - _Robert G. Wilson v_, Dec 23 2017
%C A025587 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 A025587 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 A025587 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%t A025587 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 A025587 (C)
%o A025587 // First column is this sequence.
%o A025587 // Second column is the maximum (even) N reached.
%o A025587 // Third column is A061523, the ratio of those.
%o A025587 // NOTE: This could be made faster by special-casing 1,
%o A025587 // starting at 3, and incrementing by 4, since all terms except 1
%o A025587 // are congruent to 3 (mod 4).
%o A025587 #include    <stdio.h>
%o A025587 long long    i=1, n, max_n;
%o A025587 long double    max_ratio=1.0, ratio;
%o A025587 int main()
%o A025587 {
%o A025587     while(1)
%o A025587     {
%o A025587         n = i;
%o A025587         max_n = n;
%o A025587         while (n > i) // Can stop as soon as we drop below start.
%o A025587         {
%o A025587             n = 3*n + 1;
%o A025587             max_n = (n > max_n) ? n : max_n;
%o A025587             while (!(n&1))
%o A025587             {
%o A025587                 n >>= 1;
%o A025587             }
%o A025587          }
%o A025587         ratio = (double) max_n / (double) i;
%o A025587         if (ratio > max_ratio)
%o A025587         {
%o A025587             max_ratio = ratio;
%o A025587             printf("%lld\t%lld\t%Lf\n", i, max_n, max_ratio);
%o A025587         }
%o A025587         i += 2;
%o A025587     }
%o A025587 }
%o A025587 // _Howard A. Landman_, Nov 14 2017
%Y A025587 Cf. A295163 for maximum odd number reached, and A061523 for blowup factors.
%Y A025587 Cf. A006884, A070165.
%K A025587 nonn,nice
%O A025587 0,2
%A A025587 _David W. Wilson_
%E A025587 More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001
%E A025587 a(27) from _Jud McCranie_, Apr 23 2012
%E A025587 a(26) corrected (was missing least significant digit) by _Howard A. Landman_, Nov 14 2017