# A sequence puzzle

Joseph Biberstine jrbibers at indiana.edu
Mon Jul 31 23:32:40 CEST 2006

```For fellow decipherers, here are some basic diagnostics.  Some are as
attached images.  I'll let you figure out what the images are.

the set
{1, 2, 6, 12, 60, 3, 21, 168, 504, 2520, 27720, 4, 52, 364, 5460, 21840,
371280, 1113840, 21162960, 5, 105, 2310, 53130, 212520, 1062600,
13813800, 124324200, 7, 203, 6090, 188790, 3020640, 33227040, 564859680,
35, 1260, 46620, 885780, 11515140, 10}

split into increasing runs
{1, 2, 6, 12, 60}, {3, 21, 168, 504, 2520, 27720}, {4, 52, 364, 5460,
21840, 371280, 1113840, 21162960}, {5, 105, 2310, 53130, 212520,
1062600, 13813800, 124324200}, {7, 203, 6090, 188790, 3020640, 33227040,
564859680}, {35, 1260, 46620, 885780, 11515140}
Within these runs, terms seem to rise exponentially.

dips occur at
{1, 6, 12, 20, 28, 35, 40}

successive ratios
{2, 3, 2, 5, 1/20, 7, 8, 3, 5, 11, 1/6930, 13, 7, 15, 4, 17, 3, 19,
1/4232592, 21, 22, 23, 4, 5, 13,  9, 1/17760600, 29, 30, 31, 16, 11, 17,
1/16138848, 36, 37, 19, 13, 1/1151514}

JRB

franktaw at netscape.net wrote:
> Here are the first 20 terms of a sequence:
>
> 1,2,6,12,60,3,21,168,504,2520,27720,4,52,364,5460,21840,371280,1113840,21
> 162960,5
>
> The puzzle is to determine the rule of formation.
>
>
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```