[seqfan] (no subject)
c.zizka at email.cz
c.zizka at email.cz
Tue Nov 10 09:59:31 CET 2009
Hi Paul,
yes, I corrected the wrong formula yesterday in my next email.
Is it important to look after differences to squares like i = ceiling(sqrt(f(n)))^2 - f(n) ?
I looked at f(n) = n*(n+1) / k, n*n / k, n / k , where k is a rational number , n,i positive integers.
Found :
for given values i , k lot of sequences in OEIS can be described in the form "n such that i = ceiling(sqrt(f(n)))^2 - f(n)".
For f(n) = n*n / k the sequence of n-s for a given value i is described as a(n) = 6*a(n-1)-a(n-2) ; input [a(0);a(1)] integers.
For f(n) = n / k the sequence of n-s for a given value i is described as a(n) = 2*n*n - 2*i .
For f(n) = n*(n+1) / k the sequence of n-s for a given value i is described as a(n) = t_1 * a(n-1) + ... + t_r * a(n-r) + t_s ; parameters t_y are integers (not necessarily positive).
Thats what I found so far.
Ctibor
> ------------ Původní zpráva ------------
> Od: Raff, Paul <praff at math.rutgers.edu>
> Předmět: [seqfan] Re: (no subject)
> Datum: 09.11.2009 17:40:25
> ----------------------------------------
> Hi Ctibor,
>
> I think you mean the following (with modification in caps):
>
> a(n)= ceiling(SQRT(n*(n+1)/2))^2 - n*(n+1)/2
>
> [paul]
>
> ---
> Paul Raff
> Postdoctoral Researcher - Cognitive Assistants as Analysts' Deputies
> School of Communication and Information
> Rutgers University
> http://www.myraff.com
> Work: (732) 932-7500 x8023
> Mobile: (704) 604-2154
>
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