[seqfan] Re: A024812

[Susanne Wienand]

For different values of m I get

m    floor(cot(pi/2m))
------------------------------
 1       0   *
 2       1
 3       1
 4       2   *
 5       3
 6       3
 7       4   *
 8       5
 9       5
10      6
11      6
12      7   *
13      8
14      8
15      9   *
16     10
17     10
18     11  *
19     12
20     12
21     13
22     13
23     14 *
24     15
25     15
26     16  *
27     17
28     17

Picking the values with unique floor function (marked by *) yields

m    n
--------
1     0
4     2
7     4
12   7
15   9
18  11
23  14
26  16

Except for the value n=0, n matches so far with A024812. It seems wrong to
me that the first value in A024813 is zero, because division by zero is not
allowed.

Regards, Susanne



2013/3/20 L. Edson Jeffery <lejeffery2 at gmail.com>

> In fact at least the first 41 terms match. What's going on here?
>
> Ed Jeffery
>
>
>
> On Wed, Mar 20, 2013 at 12:25 AM, L. Edson Jeffery <lejeffery2 at gmail.com
> >wrote:
> I get the same sequence Robert gets: {4, 7, 12, 15, 18, 23, 26, 29, 34, 37,
> ...}.
>
> Note that adding n-1 to the n-th term above gives the sequence
>
> {4, 8, 14, 18, 22, 28, 32, 36, 42, 46, ...}
>
> and dividing the terms by two gives
>
> {2, 4, 7, 9, 11, 14, 16, 18, 21, 23, ...}
>
> which so far matches the first ten terms of A024812. Very strange. But I
> have no idea how far out this coincidence agrees.
>
> Ed Jeffery
>
> On Wed, Mar 20, 2013 at 12:25 AM, L. Edson Jeffery <lejeffery2 at gmail.com
> >wrote:
>
> > I get the same sequence Robert gets: {4, 7, 12, 15, 18, 23, 26, 29, 34,
> 37,
> > ...}.
> >
> > Note that adding n-1 to the n-th term above gives the sequence
> >
> > {4, 8, 14, 18, 22, 28, 32, 36, 42, 46, ...}
> >
> > and dividing the terms by two gives
> >
> > {2, 4, 7, 9, 11, 14, 16, 18, 21, 23, ...}
> >
> > which so far matches the first ten terms of A024812. Very strange. But I
> > have no idea how far out this coincidence agrees.
> >
> > Ed Jeffery
> >
>
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