User talk:Olivier Gérard

A046959

Dear Olivier, This sequence is very interesting. If we denote it with $a_{n},\ n=0,1,2,...$ such that

$\sin a_{n+1}>\sin a_{n}$

would be curious to find an estimate for the sequence $a_{n}$. I have tried to find an expression for $a_{n}$, even asymptotic, but is not simple. Do you know if there are scientific articles that have already faced this problem, ie finding an estimate for $a_{n}$? thank you very much

--Pierluigi Vellucci 08:15, 24 August 2014 (UTC)Pierluigi

   I have no specific references to give you but see the comments in   A046965.  As with the original A046959, it is an expression of the rational approximations of Pi.
   --Olivier Gérard 06:46, 24 August 2014 (UTC)

Dear Olivier, thanks for your reply. But, in the sequence A046965, I can not find the comments. Can you help me find them, please?

Thanks --Pierluigi Vellucci 09:15, 24 August 2014 (UTC)

Pier-Luigi,

The comment explains how this is related to convergents to Pi. If you want to find papers on asymptotic approximations to this sequence, look for research about the continued fractions of Pi.

--Olivier Gérard 09:38, 24 August 2014 (UTC)

Thanks!

--Pierluigi Vellucci 09:43, 24 August 2014 (UTC)

A015518

((-1)^(2n)+1+9^n)/4 is related to A015518 It returns a value of double the index

I'll use the 4th index as an example. -(1/4)*(-1)^4+(1/4)*3^4=20 double the index of 4 to 8, the 8th index value is -(1/4)*(-1)^8+(1/4)*3^8=1640

Now using my formula we input 4 and output the 8th index value ((-1)^(2*4)+1+9^4)/4=1640

The formula has 3^n in it, it's n%3 is 1 on odd terms and 2 on even terms. It will never be 0, so it will never be divisible by 3.

Sequence search filtering

ok, I appreciate the assist. Here's a sample. I first type "keyword:new AND prime" and get 116 results. I then modify it to "keyword:new AND prime AND -author=Zhi-Wei Sun" and get 19 results, great. However, they are all results from Sun! I must be missing some nuance, as I'm trying to xclude those entries. Please advise ....--Bill McEachen 16:07, 14 January 2014 (UTC)

---

Dear Bill,

You should not use AND in the search box unless you really want that word and you should use  : not = after keywords. Here is an example:

                     keyword:new author:"Zhi-Wei Sun"

gives you new sequences by this author and

                     keyword:new Prime -author:"Zhi-Wei Sun"

gives you new sequences on this topic but not Sun's (about 140 when I write this). --Olivier Gérard 16:17, 14 January 2014 (UTC)

---

got it, thanks!--Bill McEachen 01:47, 15 January 2014 (UTC)

Template for number triangles

In reply to the email you sent me:

Olivier Gerard <olivier.gerard@gmail.com>
	
1:12 AM (20 hours ago)
		
to me
Dear Daniel,

Is there a template I could use to automatically
format a sequence of list of numbers into a
triangle, say like this ?

1	1										
2	1	1									
3	1	1	1								
5	1	2	1	1							
11	1	5	3	1	1						
32	1	14	11	4	1	1					
114	1	42	45	19	5	1	1				

with one or several more summing and separating lines if possible.
with the lightest syntax possible (the goal is to create this automatically
from my OEIS survey code)

If not, could you help me create the two or three
I might need ?

Also, I might need a template to create links to the triangle visualisation
urls of the encyclopedia, like this 

https://oeis.org/A008550/table

What do you think about this ?


With my best regards,

Olivier

Does the {{number triangle}} template fulfills your requirements, or do you want the template to automatically figure out where to break the lines? (I will add this option right now.) — Daniel Forgues 04:37, 10 August 2016 (UTC)

For the links to the triangle visualisation urls of the encyclopedia, what about [[OEIS:/A008550/table]] which gives /A008550/table? — Daniel Forgues 04:37, 10 August 2016 (UTC)

You may use the {{triangle line breaks}} OEIS Wiki utility template to automatically generate the triangle line breaks in a sequence of integers for the {{number triangle}} template. — Daniel Forgues 06:28, 10 August 2016 (UTC)

Hello David,

Thanks for this information and the huge work on the templates and the links and the numerous examples. I don't need the template to figure out the line breaks, I can program it myself in the way I produce the input. However, it may be asking too much and probably I should make a clone of the current template to not disturb people already using it and create something minimalist for pages having numerous triangles. Actually I would like to be able

- to not display the TeX Sigma a(n) etc. rendering but just the content of the f(n) parameter

- to not display the row indices or the column indices, in any case specify the starting value.

- to change the default background colors and font size

- to not display the sum column if it is not relevant

- to change one whole column or whole row's color, one at a time to outline something

some of these features especially the last one may be a bit too much for the template syntax. - Olivier Gérard 09:10, 10 August 2016 (UTC)

Since nobody is currently using the {{number triangle}} template, I will modify it to implement the features you suggest. — Daniel Forgues 01:14, 11 August 2016 (UTC)

Implemented, as of now:

- to not display the TeX Sigma a(n) etc. rendering but just the content of the f(n) parameter Y

- specify the starting value of row indices or column indices Y

- to change the default background colors and font size Y

— Daniel Forgues 04:36, 11 August 2016 (UTC)

- to not display the sum column if it is not relevant Y — Daniel Forgues 06:40, 11 August 2016 (UTC)

Thanks a lot for all this. I believe I should now start using it in my projects and test it before you spend too much time on this. - Olivier Gérard 10:34, 11 August 2016 (UTC)

- to not display the row indices or the column indices Y (although the space for row indices or column indices is not freed up) — Daniel Forgues 07:47, 12 August 2016 (UTC)

Now, to implement

- to change one whole column or whole row's color, one at a time to outline something

I would have to add {{#switch: }} for every triangle cell, which will likely get the MediaWiki server to balk (refuse to render...) due to an excess of parser function calls. The template is already getting slower... — Daniel Forgues 07:47, 12 August 2016 (UTC)

I will make (now done) a template for a {{highlighted number triangle}} with up to 8 (maybe 12 later) 12 rows (instead of up to 16 rows) with the following optional parameters:

• highlight style = highlight style
• highlight = highlight

where

• highlight style defaults to: background: #EEEEEE; color: black; background: #AAAAAA; color: black;
• highlight is a comma separated list of items a single item chosen from:

• r0, r1, r2, ... r0 to r11 (highlight those rows a single row) Y
• c0, c1, c2, ... c0 to c11 (highlight those columns a single column [of rectangular triangle]) Y
• central (highlight central coefficients) Y
• d0, d1, d2, ... d0 to d11 (highlight those downwards diagonals a single downwards diagonal) Y
• e0, e1, e2, ... e0 to e11 (highlight those downwards slope 1/2 diagonals a single downwards slope 1/2 diagonal) (I'm doing it...) (done) Y
• e (highlight all downwards slope 1/2 diagonals) Y
• u0, u1, u2, ... u0 to u11 (highlight those upwards diagonals a single upwards diagonal) Y
• v0, v1, v2, ... v0 to v11 (highlight those upwards slope 1/2 diagonals a single upwards slope 1/2 diagonal) Y
• v (highlight all upwards slope 1/2 diagonals) Y

What do you think? Any suggestions? — Daniel Forgues 21:57, 12 August 2016 (UTC) — Daniel Forgues 04:01, 18 August 2016 (UTC)