The Factorial Basis

IWETHEY v. 0.3.0 | TODO

1,095 registered users | 0 active users | 0 LpH | Statistics
Login | Create New User

Welcome to IWETHEY!

Post #108,183

Picture of deSitter

7/2/03 10:15:03 AM

The Factorial Basis

Instead of expanding in powers of some integer, we expand in factorials, thus

N = Ak*k! + Ak-1*(k-1)! + ... + A1*1!

with Am <= m. So for example

100 = 4*4! + 0*3! + 2*2! + 0*1! = 4020f

The last number before a rollover of digits is [n][n-1][n-2]...[1]f and represents (n+1)!-1.

In this basis you are 24 + 6 + 2 = 1*4! + 1*3! + 1*2! + 0*1! = 1110f.

Here are all the primes up to 719 = 6! - 1 = 54321f

\n0 0 0 1 0\n0 0 0 1 1\n0 0 0 2 1\n0 0 1 0 1\n0 0 1 2 1\n0 0 2 0 1\n0 0 2 2 1\n0 0 3 0 1\n0 0 3 2 1\n0 1 0 2 1\n0 1 1 0 1\n0 1 2 0 1\n0 1 2 2 1\n0 1 3 0 1\n0 1 3 2 1\n0 2 0 2 1\n0 2 1 2 1\n0 2 2 0 1\n0 2 3 0 1\n0 2 3 2 1\n0 3 0 0 1\n0 3 1 0 1\n0 3 1 2 1\n0 3 2 2 1\n0 4 0 0 1\n0 4 0 2 1\n0 4 1 0 1\n0 4 1 2 1\n0 4 2 0 1\n0 4 2 2 1\n1 0 1 0 1\n1 0 1 2 1\n1 0 2 2 1\n1 0 3 0 1\n1 1 0 2 1\n1 1 1 0 1\n1 1 2 0 1\n1 1 3 0 1\n1 1 3 2 1\n1 2 0 2 1\n1 2 1 2 1\n1 2 2 0 1\n1 2 3 2 1\n1 3 0 0 1\n1 3 0 2 1\n1 3 1 0 1\n1 3 3 0 1\n1 4 1 0 1\n1 4 1 2 1\n1 4 2 0 1\n1 4 2 2 1\n1 4 3 2 1\n2 0 0 0 1\n2 0 1 2 1\n2 0 2 2 1\n2 0 3 2 1\n2 1 0 2 1\n2 1 1 0 1\n2 1 2 0 1\n2 1 2 2 1\n2 1 3 0 1\n2 2 0 2 1\n2 2 3 0 1\n2 2 3 2 1\n2 3 0 0 1\n2 3 0 2 1\n2 3 3 0 1\n2 4 0 0 1\n2 4 1 2 1\n2 4 2 0 1\n2 4 2 2 1\n2 4 3 2 1\n3 0 1 0 1\n3 0 2 0 1\n3 0 3 0 1\n3 0 3 2 1\n3 1 0 2 1\n3 1 2 0 1\n3 1 2 2 1\n3 2 0 0 1\n3 2 1 2 1\n3 2 2 0 1\n3 2 3 2 1\n3 3 0 0 1\n3 3 1 0 1\n3 3 1 2 1\n3 3 2 2 1\n3 4 0 0 1\n3 4 0 2 1\n3 4 1 0 1\n3 4 1 2 1\n3 4 3 2 1\n4 0 1 0 1\n4 0 1 2 1\n4 0 3 0 1\n4 0 3 2 1\n4 1 0 2 1\n4 1 2 2 1\n4 1 3 0 1\n4 2 2 0 1\n4 2 3 0 1\n4 3 0 2 1\n4 3 1 2 1\n4 3 2 2 1\n4 3 3 0 1\n4 4 0 0 1\n4 4 1 2 1\n4 4 2 2 1\n4 4 3 2 1\n5 0 0 0 1\n5 0 1 0 1\n5 0 2 0 1\n5 0 2 2 1\n5 0 3 0 1\n5 1 1 0 1\n5 1 2 2 1\n5 1 3 0 1\n5 1 3 2 1\n5 2 0 2 1\n5 2 1 2 1\n5 2 2 0 1\n5 3 0 0 1\n5 3 0 2 1\n5 3 1 2 1\n5 3 3 0 1\n5 4 0 2 1\n5 4 2 0 1\n5 4 3 2 1\n

I suspect this basis could be useful in studying primes.

-drl

Post #108,184

Picture of pwhysall

7/2/03 10:17:16 AM

And this delays the mid-life crisis how?

Sorry, dude, but unless you can cook up eternal youth out of that lot, you're going to have a tough sell on your hands.

Peter
[link|http://www.debian.org|Shill For Hire]
[link|http://www.kuro5hin.org|There is no K5 Cabal]
[link|http://guildenstern.dyndns.org|Blog]

Just turned 20 - (cwbrenn) - (24) - July 2, 2003, 07:46:23 AM EDT

Old Fart. - (pwhysall) - (3) - July 2, 2003, 07:49:52 AM EDT

Looks better in hex? - (andread) - (2) - July 2, 2003, 08:05:21 AM EDT

In hex? - (pwhysall) - (1) - July 2, 2003, 08:14:32 AM EDT

Re: In hex? - (andread) - July 2, 2003, 03:10:49 PM EDT

Well, then I just turned 27 - (gdaustin) - July 2, 2003, 08:03:47 AM EDT

That makes me approximately 20.8. :-) -NT - (static) - July 2, 2003, 08:11:04 AM EDT

Me? I'm 24. -NT - (jake123) - July 2, 2003, 09:03:46 AM EDT

The Factorial Basis - (deSitter) - (1) - July 2, 2003, 10:15:03 AM EDT

And this delays the mid-life crisis how? - (pwhysall) - July 2, 2003, 10:17:16 AM EDT

074 - in octal . . . - (Andrew Grygus) - (6) - July 2, 2003, 11:19:45 AM EDT

Actually... - (pwhysall) - July 2, 2003, 11:22:13 AM EDT

hmmm... 040 - (cwbrenn) - July 2, 2003, 11:28:50 AM EDT

0x2C, huh? - (gdaustin) - (3) - July 2, 2003, 12:50:42 PM EDT

It's called survival of the fittest. - (Andrew Grygus) - (2) - July 2, 2003, 01:26:54 PM EDT

Conversion error - (jbrabeck) - (1) - July 2, 2003, 02:56:48 PM EDT

Oops.... - (gdaustin) - July 2, 2003, 03:03:27 PM EDT

Only 21 - (jbrabeck) - July 2, 2003, 12:41:07 PM EDT

Happy Birthday... - (bepatient) - July 2, 2003, 05:03:32 PM EDT

I'm an old fart - (Silverlock) - (3) - July 2, 2003, 10:33:10 PM EDT

0x32 as of April 8th. The Shadow knows! :) -NT - (a6l6e6x) - (2) - July 2, 2003, 10:36:50 PM EDT

The shadow is wrong. - (Silverlock) - (1) - July 2, 2003, 10:50:38 PM EDT

OK. Going by "almost 50" comment of yours a while back. -NT - (a6l6e6x) - July 2, 2003, 11:19:49 PM EDT

Happy Birthday! I'm 1,112. - (Another Scott) - (1) - July 3, 2003, 07:57:43 AM EDT

I'm 11111 - (inthane-chan) - July 3, 2003, 10:31:13 AM EDT

Heard that when you play a Windows CD backwards, it plays satanic message? That's nothing! When you play it forward, it installs Windows!
46 ms