[Search for users]
[Overall Top Noters]
[List of all Conferences]
[Download this site]
| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
95.0. "STAT'L PROP'S OF PALINDROMIC SEQ" by METOO::YARBROUGH () Wed Jul 25 1984 18:08
Here's an open question for anyone who's interested.
A fair amount of investigation has gone into the question whether the
following process always produces a palindrome: start with an integer and add
it to its reversal. If th sum is not (yet) a palindrome, repeat the reversal
and addition, etc. It is known, for example, that all integers up to 196
produce palindromes fairly quickly, but that 196 does not.
I'm not really interested in the palindromes, but in the statistical
properties of the digits that occur in the process. I have run the process
(ignoring whether or not palindromes are produced) for many starting
integers and for many thousands of cycles and found that the frequency
distribution of the digits is NOT normal; instead, complementary digits
(0/9, 3/7, etc) appear with equal frequencies, but the pairs do not. For
example, 0/9's appear about 5% more frequently than 1/8's. This (5%)
figure is consistent and independent of the starter and (above a reasonable
threshold) the number of cycles.
Problem: what is the underlying process that results in this skewed frequency
distribution?
Observation (which may or may not be relevant): The reversal/summing process
also produces an abnormally large number of multiple digits, e.g. ...3333....
Lynn Yarbrough
| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 95.1 | What's the difference between ignorance and apathy? | AKQJ10::YARBROUGH | I prefer Pi | Wed Oct 18 1989 15:48 | 5 |
| After over five years with no replies, this is still an open question...
Looks like I'll have to find my old code that I used to investigate this
problem and publish an example or two.
Lynn Yarbrough
|
| 95.2 | Here's what it looks like | AKQJ10::YARBROUGH | I prefer Pi | Wed Oct 18 1989 18:25 | 15 |
| In running the process until a number 10,000 digits long is produced, the
count of digits looks like:
Dig Freq Freq Dig
0 10467078 10473132 9
1 9909301 9914472 8
2 10042166 10045884 7
3 9884021 9882557 6
4 10105321 10105782 5
The complementary digits are within .05% of each other, but 0/9 is more
frequent than 3/6 by about 6%, which is statistically very significant
at this sample size.
Any clues?
|
| 95.3 | | RUSURE::RABAHY | dtn 381-1154 | Thu Oct 19 1989 14:41 | 1 |
| What happens in other bases?
|
| 95.4 | Much the same for base 8 | AKQJ10::YARBROUGH | I prefer Pi | Mon Oct 23 1989 17:31 | 12 |
| For radix=8, running until a 1000-digit number is produced, the digits
occur with these frequencies:
0 164505 165080 7
1 153933 153750 6
2 156370 156580 5
3 156118 156101 4
Again, complementary digits have roughly equal frequencies, but freq(1)<<
freq(0).
Lynn
|