Aspies For Freedom

What is your favorite number, and why?
(Not just whole numbers.  You can have rational, irrational, or even hexadecimal numbers too, if you prefer.)


My favorite number is 156 because it is the product of 12 and 13, both of which hold great significance in everyday life and throughout history in the realms of mathematics, time, astrology, superstitions, religion, geometry, entertainment, and American symbolism.  

I also really like pi.  I have memorized its first 200 decimal places, but I'll stop there for a while so I can devote more effort to memorizing prime numbers.

Had I been cool, I might have said 1729 or even 42, to show my belonging to the cool in-crowd that gets it (anyone else?).

But in reality, I've a curious fascination for powers of two: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536...I don't know why I have the sequence stuck in my head, but it's there. Perhaps that makes it my "favorite number series" -- as if that gives much meaning.

I like seven! I always have... it just seems so... calm.

I hate six. It's not quite "a lot" but it's not quite "a little", and it's not half... it's like it's constantly thrashing... or like it doesn't belong there.

I love that sequence! I think I was 9 or 10 when I calculated it by adding each number to itself.  I did it on the old fan-fold printer paper with the small holes on the sides, continuously on several pages until the number got so big that I ran out of room.  I was fascinated with the repeating pattern of the last digits (...2 4 8 6 2 4 8 6...).  

A similar experience at age 13: We got our first computer at home (with Windows 3.1 ), and I used the MS-DOS edit program to type all binary numbers from 0 to 100000000000 (that's 2048 in decimal).

Whoa. Never noticed that.

I, too, remember calculating this and writing it down when I was maybe 8-9, thereabouts. The ones I listed are the ones that are more or less in my head. 2^16 (65536) is the number of combinations of a 16-bit binary number, so it's OK.

1729 is from an anecdote about mathematicians G.H. Hardy and Srinivasa Ramanujan. Hardy tells it (snitched that from wikipedia):

See, the only reason I mentioned it was so I could lecture you on it

All this talk of the 2^n sequence and the repeating pattern of 2 4 8 6 got me wondering:  Is there a repeating pattern in the tens column?  What about the hundreds column and so forth?  I would need to calculate the sequence 2 4 8 16 32 64 128 256 512 1024... until I see a pattern.

I couldn't get very far with a direct calculation on the calculator or computer because I would need to make some really BIG numbers with every digit explicitly stated.  (Actually, for this purpose, I only need the last 5 or 6 digits of each number, but I like to be consistent.)

It is easy to see on a calculator that the tens column has a repeating pattern, the first of which begins at 2^2 = 4 and ends at 2^21 = 20947152.  In fact you can see below that the two patterns in the tens an units columns are closely linked.  The tens pattern begins at n = 2, 22, 42, 62, etc.  Each of those numbers (2^2, 2^22, 2^42, 2^62,...) end with 04.  So the repeating pattern we have here is 04, 08, 16, 32, 64, 28, 56, 12, 24, 48, 96, 92, 84, 68, 36, 72, 44, 88, 76, 52.  

   2^n        n
-----------------
00000002   1
00000004   2  <-- tens pattern begins
00000008   3
00000016   4
00000032   5
00000064   6
00000128   7
00000256   8
00000512   9
00001024  10
00002048  11
00004096  12
00008192  13
00016384  14
00032768  15
00065536  16
00131072  17
00262144  18
00524288  19
01048576  20
02097152  21  <-- tens pattern ends
04194304  22  <-- tens pattern repeats
08388608  23
16777216  24
...

I used Excel for the really big number crunching.  I started with 2, then wrote a formula to find each digit in its own individual cell.  I assumed that the hundreds pattern would be 100 numbers long.  Consider the units pattern (2 4 8 6) is four numbers long.  The tens pattern (04 08 ... 76 52)  is 20 numbers long.  4 * 5 = 20.  So I did 20 * 5 = 100.  I also assumed that it would start with 2^3 = 008 since the tens pattern starts with 2^2 = 04 and the ones pattern starts with 2^1 = 2.

Sure enough, I got first repetition of the hundreds pattern at
2^103 =
10141204801825835211973625643008

I then derived that each pattern has length
L = 5^C - 5^(C-1)
where C is the column number, beginning with C = 1 for units, C = 2 for tens, C = 3 for hundreds, etc.

Also, each pattern has its first repetition at
n = L + C

For the thousands pattern, we have
C = 4
L = 5^4 - 5^3 = 500
n = 500 + 4 = 504

So the thousands pattern is 500 numbers long, begins at 2^4 = 0016 and repeats at
2^504 = 52374249726338269920211035149241586435466272736689036631732661889538140742474792 878132321477214466514414186946040961136147476104734166288853256441430016

By the way, when I say "500 numbers long", I mean all the numbers from 2^4 to 2^503.  The above number for 2^504 is 152 digits long.

Before using Excel, I calculated 2^121 by hand, some of it in my head, and some of it in 12 digit chunks with my TI-89 calculator.  I got the final answer terribly wrong, though, because I missed carrying a 1, half way through.

Thus I have spent a good chunk of my weekend calculating 2^504 JUST FOR FUN !
Take THAT, neurotypicals !!!

I like odd numbers.  Especially nine and multiples of nine (I have a few little OCD-type rituals centered around them.)

Any multiple of nine, when the numbers are added together, boils down to nine.

9 x 2 = 18  1 + 8 = 9
9 x 3 = 27  2 + 7 = 9
9 x 4 = 36  3 + 6 = 9....

then it gets better, with more steps:

11 x 9 = 99  9 + 9 = 18  1 + 8 = 9
12 x 9 = 108  1 + 0 + 8 = 9
13 x 9 = 117  1 + 1 + 7 = 9.....

As far as I know, this doesn't work with multiples of any other number.

I also like the "4 8 15 16 23 42" sequence from "Lost".  (The show is a special interest....and the sum of those numbers is 108. 1 + 0 + 8 = 9   )

I think there's actually at least one if not more forums devoted entirely to the speculation on the Lost numbers. Talk about devotion!

Well, can't find it now, but I distinctly remember visiting a web forum about them, anyway. Perhaps it doesn't exist any more.

^That's almost as good as the multiples of nine series  

number 13. If its my favourite number, it cant be unlucky for me!

42!!!! It's the meaning of life!

Elevenses and Eleventy-One, as with most palindromic numbers, are very "Hobbit forming".
111^2=12321
111^3=1367631
1111^2=1234321
11111^2=123454321
111111^2=12345654321
1111111^2=1234567654321
11111111^2=123456787654321
111111111^2=12345678987654321
Here's a way to waste an afternoon:
Take a three digit number, reverse the digits and add them,
take the sum, reverse the digits and add, repeat this process
until you get a Palindromic Number, Examples:
195+591=786
786+687=1473
1473+3741=5214
5214+4125=9339
9339 is palindromic.
Let's try this with 197:
197+791=988
988+889=1877
1877+7781=9658
9658+8569=18227
18227+72281=90508
90508+80509=171017
171017+710171=881188
881188 is palindromic
Try this process for 196 and you will waste more than an afternoon,
196 does not form any palindromes at all.
There are many of these Lychrel Numbers that have vexed many of us number buffs. Enjoy!!
Number 89 has some interesting properties. For further reading check out:
http://primes.utm.edu/top20/page.php?id=53
http://www.mathematische-basteleien.de/palindromes.html

Also one of my favorites: 17
Primes of form n^2+n+17.
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