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A025587
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'3x+1' record-setters (blowup factor).
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3
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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
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OFFSET
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0,2
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COMMENTS
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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
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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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;
}
}
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CROSSREFS
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Cf. A295163 for maximum odd number reached, and A061523 for blowup factors.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 03 2001
a(26) corrected (was missing least significant digit) by Howard A. Landman, Nov 14 2017
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STATUS
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approved
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