A129894, patterns, randomness, and clumps

[Jon Schoenfield]

Dear SeqFans,

On looking through some of the newest sequences in the OEIS, I ran across 
A129894:

<<  If "sumdigit" denotes the sum of the digits of a number then these are 
the numbers n such that [sumdigit(n!) mod n]=0.  >>

(The offset is shown as 0, but given a reminder that Neil had sent to the 
list fairly recently, I'd have thought the offset for such a sequence would 
be 1....)

At any rate, the terms I've obtained thus far are

1, 2, 3, 9, 15, 18, 21, 27, 72, 81, 234,
462, 502, 522, 1314, 1323, 3789, 3897,
6462, 10470, 17532, 17820, 28503,
48248, 48254, 48303, 48644, 48856

(with the next term somewhere beyond 180000).

I realize that even a randomly-generated sequence may be perceived as 
exhibiting a pattern, so I didn't think it too odd the way many of the 
larger numbers seemed to be falling into "clumps" of two or more; e.g., on a 
logarithmic scale, 462, 502, & 522 are fairly close together, as are 1314 & 
1323, 3789 & 3897, and 17532 & 17820.  Still, 234, 6462, 10470, and 28503 
looked rather lonely.  Just when I was ready to dismiss the perceived 
clumping of terms as being of no particular significance, my program 
generated five terms, all in the 48 thousands!  (Hmmmm ....)

This got me thinking about a broader question:  How do you decide whether 
some observed behavior of a deterministic sequence -- some perceived 
pattern -- seems sufficiently significant that you think it's worth offering 
a conjecture to your colleagues about that behavior?  Do you apply some sort 
of statistical test(s)?  Is it more a matter of what some might call a "gut 
feeling," based partly on what you know about the sequence thus far, and 
partly on prior experiences with a variety of sequences?  And does any 
confidence you might place in "gut feelings" about sequences in general tend 
to get shaken when something very surprising turns up regarding some other 
problem, e.g., the discovery of "Numbers n such that ceiling( 
2/(2^{1/n}-1) ) is not equal to floor( 2n/(log 2) )" (i.e., terms in 
A129935)?

... My apologies if these are obviously dumb newbie questions!  ?:-|

Thanks for your time,

-- Jon






Dear Seqfans,  I've just updated 3 seqs that were discussed
here recently:

A129935
A080754
A080755
and i killed A120754 and -5

new version of OEIS in 10 mins

Thanks to everyone who sent comments



]
Dear Seqfans, please let's keep the discussions here
on a friendly basis!  We are all friends here.
Negative comments about others are not appropriate.
Neil