# [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
>

```