[seqfan] Re: About A090503 Number of hyperplanes

Wouter Meeussen wouter.meeussen at telenet.be
Wed Nov 20 17:29:59 CET 2013

```I can confirm Jean-François' results.

It seems like the original submision did not extend the range of 'd' far
enough.

The links in A090503 are 'pining for the fjords' and so quite unresponsive.

A slightly more extended search:

uni = Sort@ Flatten at Table[((p^m)^(d + 1) - 1)/(p^m - 1), {d, 2, 36}, {m, 1,
16}, {p, Prime /@ Range[999]}];
Select[Range[5000], MemberQ[uni, #] &]

{7,13,15,21,31,40,57,63,73,85,91,121,127,133,156,183,255,273,307,341,364,
381,400,511,553,585,651,757,781,820,871,993,1023,1057,1093,1365,1407,
1464,1723,1893,2047,2257,2380,2451,2801,2863,3280,3541,3783,3906,4095,
4161,4369,4557,4681}

Wouter.

-----Original Message-----
From: Neil Sloane
Sent: Wednesday, November 20, 2013 4:34 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: About A090503 Number of hyperplanes

Well, I do know something about the subject, and the
formula:

Numbers of the form (q^(d+1)-1)/(q-1), d>=2, q=p^m with m>=1 and p prime

is correct! Compute all numbers of that form,
remove duplicates, and sort them into increasing order.

But I don't know much about Mathematica, so I can't check your program. If
it is doing
what the formula says, then your version is correct,
and A090503 should be changed.

I wonder if the incorrect sequence is given in any of the references? If so
we might
make a new entry for the wrong sequence,
since the OEIS policy is to include published sequences that are wrong
(giving a pointer to the correct entry).

Neil

On Wed, Nov 20, 2013 at 10:16 AM, Jean-François Alcover <
jf.alcover at gmail.com> wrote:

> Dear SeqFans,
>
> While checking A090503 (without knowing anything about the subject)
> I spotted missing terms, assuming the formula meant "All numbers of the
> form".
> For instance 127 = ((2^1)^(6 + 1) - 1)/(2^1 - 1) is missing,
>        though 63 = ((2^1)^(5 + 1) - 1)/(2^1 - 1) is present.
> Same trouble with 255, 511, 1023, 1093, 2047, 3280, 4095, ...
> I presume the formula actually meant "Some numbers of the form".
> Any idea?
>
> J.-F. Alcover
>
> p.s. This is the way I did it with Mma:
>
> f[n_] := Do[If[n == ( (p^m)^(d + 1) - 1)/( p^m - 1), Print[{n, d, m, p}];
>    Return[True]], {d, 2, 11}, {m, 1, 6}, {p, Prime /@ Range[18]}]
>
>  Select[Range[200], f[#] === True &]
>
>  {7,2,1,2}
>
>  {13,2,1,3}
>
>  {15,3,1,2}
>
>  {21,2,2,2}
>
>  {31,2,1,5}
>
>  {40,3,1,3}
>
>  {57,2,1,7}
>
>  {63,5,1,2}
>
>  {73,2,3,2}
>
>  {85,3,2,2}
>
>  {91,2,2,3}
>
>  {121,4,1,3}
>
>  {127,6,1,2}
>
>  {133,2,1,11}
>
>  {156,3,1,5}
>
>  {183,2,1,13}
>
>  {7, 13, 15, 21, 31, 40, 57, 63, 73, 85, 91, 121, 127, 133, 156, 183}
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

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```