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My favorite integer sequence
#19
Some Top posters of the tetration forum :

Bo " administrator " 198214
Tommy " sinh " 1729
Gottfried " matrix " Helms
Jay "excel" fox
sheldon " theta wave "
mike "continuum sum " 3
Jms " transform " Nxn

Ive been wanting to post that silly thing for a long time Smile

Anyway the posts made by Gottfried and Jay look familiar to me.
I also used excel to accelerate the computation of the sequence and investigate its number theoretic properties.
I Always factor number sequences.


Anyways a few remarks/ideas :

1) Many years ago I mentioned the equations

A) f ' (2x) = 3 f(x) + C
B) f ' (x) = f(x/2) + f(x/3) + C

at , if im not mistaken , sci.math.

Seeing Jay's f ' (2x) = f(x) makes me wonder about those again.
Unfortunately I have holes in my brain.

2) Our sequence satisfies f(n) - f(n-1) - (f(n-1) - f(n-2)) = f(n-2) or similar if we IGNORE ZERO. I havent quite made that clear before.

3) What I was really looking for is a closed form expression for the sequence.
Some transformation or such like for the gamma function.

4) I would like a single functional equation for the series that is exact and does NOT use rounding. If possible.

5) I would like to comment that f(x) - f(x-1) can Always be approximated by
f(x) - ( f(x) - f ' (x) + f '' (x)/2 - f "' (x)/6 + f ""(x)/24 )

Hence differences / difference equations can be approximated by differential / differential equations.

This might be usefull as it has been in the past.
Maybe it can connect Jay's f(x) with the Original sequence , maybe express one in terms of the other or solve 3) or 4).

Those are the most important things for me.

regards

tommy1729
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Messages In This Thread
My favorite integer sequence - by tommy1729 - 07/27/2014, 08:44 PM
RE: My favorite integer sequence - by jaydfox - 07/31/2014, 01:51 AM
RE: My favorite integer sequence - by jaydfox - 08/01/2014, 01:53 AM
RE: My favorite integer sequence - by Gottfried - 08/01/2014, 03:25 PM
RE: My favorite integer sequence - by jaydfox - 08/01/2014, 05:04 PM
RE: My favorite integer sequence - by sheldonison - 08/01/2014, 11:36 PM
RE: My favorite integer sequence - by jaydfox - 08/01/2014, 11:57 PM
RE: My favorite integer sequence - by jaydfox - 08/05/2014, 04:49 PM
RE: My favorite integer sequence - by jaydfox - 08/05/2014, 05:57 PM
RE: My favorite integer sequence - by Gottfried - 08/06/2014, 04:38 PM
RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:19 AM
RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:34 AM
RE: My favorite integer sequence - by jaydfox - 08/09/2014, 09:42 AM
RE: My favorite integer sequence - by Gottfried - 08/09/2014, 02:27 PM
RE: My favorite integer sequence - by tommy1729 - 09/09/2014, 12:55 AM
RE: My favorite integer sequence - by jaydfox - 08/08/2014, 12:55 AM
RE: My favorite integer sequence - by Gottfried - 08/08/2014, 02:27 AM
RE: My favorite integer sequence - by jaydfox - 09/09/2014, 07:43 PM
RE: My favorite integer sequence - by jaydfox - 09/09/2014, 09:45 PM
RE: My favorite integer sequence - by jaydfox - 08/02/2014, 12:08 AM
RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:38 PM
RE: My favorite integer sequence - by sheldonison - 08/04/2014, 11:49 PM
RE: My favorite integer sequence - by jaydfox - 09/16/2014, 05:32 AM
RE: My favorite integer sequence - by Gottfried - 09/17/2014, 07:39 PM
RE: My favorite integer sequence - by jaydfox - 10/02/2014, 10:53 PM
RE: My favorite integer sequence - by Gottfried - 08/03/2014, 03:32 PM
RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:44 PM
RE: My favorite integer sequence - by sheldonison - 08/02/2014, 05:48 AM
RE: My favorite integer sequence - by tommy1729 - 09/10/2014, 08:57 PM
RE: My favorite integer sequence - by Gottfried - 08/02/2014, 07:43 PM
RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:29 PM
RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:36 PM
RE: My favorite integer sequence - by tommy1729 - 08/05/2014, 11:16 PM
RE: My favorite integer sequence - by tommy1729 - 08/08/2014, 11:02 PM
RE: My favorite integer sequence - by jaydfox - 08/09/2014, 07:02 PM
RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:51 PM
RE: My favorite integer sequence - by sheldonison - 08/11/2014, 04:51 PM
RE: My favorite integer sequence - by jaydfox - 08/11/2014, 05:19 PM
RE: My favorite integer sequence - by jaydfox - 08/19/2014, 01:36 AM
RE: My favorite integer sequence - by jaydfox - 08/19/2014, 02:05 AM
RE: My favorite integer sequence - by jaydfox - 08/19/2014, 05:31 PM
RE: My favorite integer sequence - by sheldonison - 08/19/2014, 07:56 PM
RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:42 AM
RE: My favorite integer sequence - by sheldonison - 08/20/2014, 02:11 PM
RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:57 PM
RE: My favorite integer sequence - by jaydfox - 08/21/2014, 01:15 AM
RE: My favorite integer sequence - by jaydfox - 08/21/2014, 05:25 AM
RE: My favorite integer sequence - by jaydfox - 08/22/2014, 05:39 PM
RE: My favorite integer sequence - by jaydfox - 09/11/2014, 01:33 AM
RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 09:16 PM
RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:19 PM
RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 10:52 PM
RE: My favorite integer sequence - by jaydfox - 08/09/2014, 11:46 PM
RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 11:10 PM
RE: My favorite integer sequence - by jaydfox - 08/10/2014, 12:30 AM
RE: My favorite integer sequence - by tommy1729 - 08/11/2014, 12:17 PM
RE: My favorite integer sequence - by Gottfried - 08/22/2014, 12:30 AM
Amazing variant - by tommy1729 - 08/26/2014, 08:57 PM
RE: My favorite integer sequence - by tommy1729 - 09/01/2014, 10:37 PM
RE: My favorite integer sequence - by tommy1729 - 10/02/2014, 11:24 PM
RE: My favorite integer sequence - by jaydfox - 10/02/2014, 11:29 PM
RE: My favorite integer sequence - by tommy1729 - 02/10/2015, 12:15 AM
RE: My favorite integer sequence - by tommy1729 - 02/15/2015, 05:19 PM
RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 08:22 AM
RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 09:10 PM
RE: My favorite integer sequence - by tommy1729 - 03/13/2016, 12:31 AM

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