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A025587 '3x+1' record-setters (blowup factor). 3
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 (list; graph; refs; listen; history; text; internal format)
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)

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

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

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

Cf. A006884, A070165.

Sequence in context: A147638 A147394 A103021 * A101498 A027965 A130145

Adjacent sequences:  A025584 A025585 A025586 * A025588 A025589 A025590

KEYWORD

nonn,nice

AUTHOR

David W. Wilson

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

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Last modified January 21 16:47 EST 2020. Contains 331114 sequences. (Running on oeis4.)