Posts by mda_
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1) Message boards : News : Back to Normal (Message 8938)
Posted 2740 days ago by mda_
*Crossing Fingers* for ya. ;) If it doesn't hold up, maybe it'll need to be slashdotted or something comparably semi-rediculous. Of course, there's no telling how much bandwidth surge you'd get from that(!) You'd probably want to put in a referrer filter/redirect. ;)
2) Message boards : News : Back to Normal (Message 8929)
Posted 2741 days ago by mda_
@Slicker: If it's not prohibited by your Comcast agreements, you could make a special page graphing all your outages....you'd either get cut off, or they'd fix that "last mile" real quick(!) ;)
3) Message boards : Science : Various Collatz Stats... (Message 8793)
Posted 2751 days ago by mda_
Some other stats that could be collected with the workunits, though it would slow the clients down...

http://www.research.att.com/~njas/sequences/?q=collatz+keyword:more&sort=0&fmt=0&language=english&go=Search

Not a suggestion to Slicker, just interesting.

~d
4) Message boards : Science : OEIS A173732 (Another Interesting Way To View The Sequence) (Message 8791)
Posted 2751 days ago by mda_
http://www.research.att.com/~njas/sequences/A173732
5) Message boards : Science : collatz parity help (Message 8693)
Posted 2757 days ago by mda_
http://www.ieeta.pt/~tos/3x+1.html
6) Message boards : Science : Largest number checked? (Message 8660)
Posted 2760 days ago by mda_
Slicker: What's the highest work unit received to date, can ya share? Taking the numbers from your posts above, it sounds like we're working in the [2^71,...) range.

(float(log(2361183346958000000001)/log(2)),float(log(2362904828965727392679)/log(2)))
-> (71.000000064475202, 71.001051515495149)

I'm sure the OEIS would love a "b-file" contribution. :-)
7) Message boards : Science : Largest number checked? (Message 8577)
Posted 2766 days ago by mda_
Ethian: it's log-linear, or at least appears to be for as far as can be quickly computed. It's easy to modify that small program I posted to change the x-axis to log(input). I misspoke though, it, of course, does not detect non-trivial cycles (counter-examples)...so it's just for fun.... :)
8) Message boards : Science : Largest number checked? (Message 8546)
Posted 2767 days ago by mda_
Here's a short Sage (python) program that searches for counterexamples, and displays a graph. It assumes your low input parameter will be 3 mod 4 since a counter-example is supposed to be 3 mod 4 (citation on wikipedia or mathworld.) I could be wrong, I skimmed it. :-) It could be more efficient...but it makes more pretty graphs.

http://www.sagemath.org/download.html

def collatz(z): i = 0 zin = z while z > 1: i = i + 1 if z % 2: z = 3 * z + 1 else: z = z / 2 return (zin, i) def mys(lo, hi): lst = [] while lo < hi: lst.append(collatz(lo)) lo += 4 return list_plot(lst) #mys(3+2^58, 3+2^59)
9) Message boards : Science : Largest number checked? (Message 8436)
Posted 2774 days ago by mda_
Ethian: Thanks for the enthusiasm and the compliment! One point of difference: you cannot prove the conjecture is true by trying all positive numbers, since they are infinite.

When I got my CS Degree ('02), I was taught there are only 3 kinds of proofs:
1) Proof by definition
2) Proof by counter-example
3) Proof by induction (inference from axioms)

There was (and perhaps still is) debate about Diagonalization being a 4th method, or just another case of induction.

What you can do, by checking higher and higher integers, is look for a counter-example (a proof that the conjecture is false).

10) Message boards : Science : Largest number checked? (Message 8340)
Posted 2780 days ago by mda_
Ethian: Yes, there are various tradeoffs you can make depending on your goals. The goal of my post was to let the curious check an arbitrary number easily. Python is an easy and interactive means to do so -- that script runs on Ubuntu if you just install the python-gmpy package, or on MacOSX with the py-gmpy package (macports). Of course, it's not designed to be particularly fast.

I don't know what kind of stats the admins keep, or if they are mostly interested in the search for a counter-example to the conjecture.
11) Message boards : Science : Largest number checked? (Message 8209)
Posted 2790 days ago by mda_
To jump ahead to arbitrarily high numbers :)

#!/usr/bin/env python # DonMorrison at gmail import sys, gmpy def collatz(z): cnt = gmpy.mpz(0) while z != 1: cnt += 1 #print '%d' % z if z % 2:#odd z = 3 * z + 1 else:#even z = z / 2 print 'Total iterations before reaching 1: %d' % cnt collatz(gmpy.mpz(sys.argv[1]))




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