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#26 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-02 02:29:29
Maybe 2013 is the smallest uninteresting number?
#27 Re: Euler Avenue » Ramanujan's pi approximation equation » 2013-01-02 00:37:06
Just in case others are wondering how I managed it, I want to check only the nearest integer. So for 2^[9999/x], I'll check 2^[9999/6055] because x = ||(9999 log(2))/(log(pi))|| = 6055. So for the rest, I'll check 2^[9998/(||9998*log(2))/(log(pi)||)]. I hope this makes sense.
#28 Re: Euler Avenue » Ramanujan's pi approximation equation » 2012-12-31 09:55:47
Just brute force with code... Just takes a second to run. I'm on my way to a NYE party of non mathematicians so I'll give you the code when I get back to my laptop sometime in the new year 
Happy New Year!
#29 Re: Euler Avenue » Ramanujan's pi approximation equation » 2012-12-31 05:23:37
Thanks for noticing that typo! I just found 5^(4333/6092)=3.1415926587376378353132531097... Which is even more accurate than 2^[9217 /5581] yet just as simple. Cool!
#30 Re: Euler Avenue » GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10 » 2012-12-31 00:55:56
I don't know how to input latex into this forum but I can tell you that if you enter 'sum_(i=1)^10 i! ; sum_(i=1)^11 i!' without quotes into the Wolfram|Alpha website or iPhone/iPad app, you will see the desired equations and their GCD.
#31 Euler Avenue » Ramanujan's pi approximation equation » 2012-12-31 00:29:42
- pellerinb
- Replies: 13
I'm sure others have made similar discoveries... I just discovered 2^[9217/5581] = 3.1415926... is more simple and more accurate than Ramanujan's pi approximation equation of 2^0.5 * 9801 / 4412 cool!
#32 Euler Avenue » GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10 » 2012-12-28 01:07:17
- pellerinb
- Replies: 3
Just curious if anyone else has observed this. I have found it true up to N = 1 million.
GCD(sum_(i=1 to N) i!, sum_(i=1 to N+1) i!) = 99 for N >= 10
I'm thinking it might be easy to prove this too... I'm not sure though.
#33 Euler Avenue » primes in sum_(i=1)^N i^i » 2012-12-28 00:44:39
- pellerinb
- Replies: 0
As far as the first 20,000 numbers, there are only 5 primes discovered in this sequence:
{1, 5, 32, 288, 3413, 50069, 873612, 17650828, 405071317, 10405071317, 295716741928, 9211817190184, 312086923782437, 11424093749340453, 449317984130199828, 18896062057839751444, 846136323944176515621, 40192544399240714091045, 2018612200059554303215024, 106876212200059554303215024, 5949463230586042075684339445, 347377340594805599472331063029, 21227845340442717633827363973596, 1354963622190726842082908836817372, 90172805592203250075973442284082997, 6246292385799360560872647730684286773, 449672780628837130509122278349834179576, 33595195893882211993081850531714439992312, 2601281349055093346554910065262730566475781, 208492413443704093346554910065262730566475781,...}
I just thought this is interesting to others :)
#34 Re: Euler Avenue » n! = ... » 2012-12-26 08:42:34
hense the edit, anonimnystefy.
#35 Euler Avenue » n! = ... » 2012-12-26 08:39:41
- pellerinb
- Replies: 6
Can any n! be represented by a sum of natural numbers {a[1], a[2], a[3] ...} raised to any power such that a[i] ≠ a[j] and 0 < a[i],a[j] <= n for all i and j?
1! = 1
2! = 2
3! = 3 + 2 + 1
4! = 4^2 + 3 + 2^2 + 1
5! = 5^2 + 4^3 + 3^3 + 2^2
6! = 5^4 + 4^3 + 3^3 + 2^2
Who knows? :)
#36 Re: Introductions » Hello from Nova Scotia » 2012-12-26 06:37:58
Thanks for that, Bob! That's pretty neat.
#37 Re: Euler Avenue » Smarandache Reverse Power Summation (SRPS) numbers » 2012-12-26 06:28:48
Absolutely. 20 / 100 implies that 20 out of the first 100 numbers are divisible by 5, etc. It's apparently a repeating pattern too, so the next 100 numbers are divisible by 5 as were the first. Entering "[Table[sum from k = 1 to T (T-k+1)^k, {T,1,200}]] mod 5" in Wolfram|Alpha shows the residues modulo 5 for the first 200 SRPS numbers.
#38 Re: Euler Avenue » Smarandache Reverse Power Summation (SRPS) numbers » 2012-12-26 06:02:16
I cannot post a download link because I am not an "established" member yet. However, google "smarandache reverse power summation numbers the free library" and it should be the first hit.
#39 Re: Maths Teaching Resources » Learning Graph Theory » 2012-12-26 05:49:56
I learned graph theory from "Graph Theory and Its Applications" by Yellen and Gross. There is some coding info in it and I found the book very readable. Perhaps your local university library has this one or similar.
#40 Euler Avenue » Smarandache Reverse Power Summation (SRPS) numbers » 2012-12-26 05:36:26
- pellerinb
- Replies: 5
I read an article about SRPS numbers and thought it would be neat to explore this sequence a little more. The article is available on the Free Online Library titled as above by Jason Earls.
I notice similarities between the set of SPRS numbers (1, 3, 8, 22, 65, ...) and the set of natural numbers (1, 2, 3, 4, 5, ...). In either set,
2/4 = 1/2 of the numbers are divisible by 2.
6/18 = 1/3 of the numbers are divisible by 3.
but 3/8 of the SPRS numbers are divisible by 4 (as opposed to 2/8 = 1/4 of the natural numbers)
yet 20/100 = 1/5 of the numbers are divisible by 5.
6/36 = 1/6 of the numbers are divisible by 6.
42/294 = 1/7 of the numbers are divisible by 7.
but 3/16 of the numbers are divisible by 8.
6/54 = 1/9 of the numbers are divisible by 9.
but 3/32 of the numbers are divisible by 16.
I conjecture that 3/2^(n+1) of the SPRS numbers are divisible by 2^n for all n > 1 and 1/m of the SPRS numbers are divisible by all other numbers m not represented by 2^n.
Perhaps you find this interesting too. Thanks in advance for your comments, corrections and the like!
Sincerely,
Brian Pellerin, MSc Dalhousie
#41 Introductions » Hello from Nova Scotia » 2012-12-26 05:19:34
- pellerinb
- Replies: 6
Hi Everyone! 
I have been enjoying math ever since high school. I love primes and consider any composite number like a molecule composed of distinct prime factors. I like to represent numbers a couple dozen or hundred digits long by simple expressions and consider it like "exploring space with a telescope". Discovering weird sequences fascinate me; right now I am enjoying the Smarandache Reverse Power Summation numbers. I've got a BSc in math and a MSc in agricultural math modelling from Dalhousie. I slavishly use Wolfram|Alpha for spontaneous calculations and occasionally program with R.
I just discovered this website so I have no clue what the focus or interests of others are yet. Math IS fun!!