[seqfan] Re: Rank of n in the Odd/Even sequence

Eric Angelini Eric.Angelini at kntv.be
Tue Feb 3 20:13:43 CET 2009

Waow, Alois !
(thanks to the others, too!)
I will only publish this on my website in a couple of days.
I'll keep you informed.
Best,
É.

-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu]
De la part de Prof. Dr. Alois Heinz
Envoyé : mardi 3 février 2009 18:58
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Rank of n in the Odd/Even sequence

Eric Angelini schrieb:

> Is the hereunder idea 'chaff' ?

Yes, it is.

>I have computed this array yesterday (by hand):
>
> S(1) =  1, 1,  6,   58,     5829,    58292915, ...
> S(2) =  2, 1, 11, 1056, 10555528, ...
> S(3) =  3, 2, 16, 1608, 16080804, ...
> S(4) =  4, 2, 21, 2111, 21106056, ...
> S(5) =  5, 3, 27, 2664, 26636332, ...
> S(6) =  6, 3, 32, 3166, 31661583, ...
> S(7) =  7, 4, 37, 3719, 37186860, ...
> S(8) =  8, 4, 42, 4221, 42212111, ...
> S(9) =  9, 5, 48, 4774, 47742387, ...
>S(10) = 10, 5, 53, 5277, 52767639, ...
>
>Could someone extend this array (to the right) -- or at least S(1)?
>
>
>
But with the help of a tiny Maple Program ...

rank:= n-> `if` (type(n, 'even'), n/2, (n+1)/2);
a := proc (n,k) option remember;
if n=1 then k
else rank (parse (cat(seq(a(j,k), j=1..n-1))))
fi
end;

for k from 1 to 10 do  lprint (seq(a(n,k), n=1..7)) od ;

1, 1, 6, 58, 5829, 58292915, 5829291479146458
2, 1, 11, 1056, 10555528, 1055552805277764, 10555528052777640527776402638882
3, 2, 16, 1608, 16080804, 1608080408040402, 16080804080404020804040204020201
4, 2, 21, 2111, 21106056, 2110605560553028, 21106055605530281055302780276514
5, 3, 27, 2664, 26636332, 2663633213318166, 26636332133181661331816606659083
6, 3, 32, 3166, 31661583, 3166158315830792, 31661583158307916583079157915396
7, 4, 37, 3719, 37186860, 3718685968593430, 37186859685934301859342984296715
8, 4, 42, 4221, 42212111, 4221211071106056, 42212110711060557110605535553028
9, 5, 48, 4774, 47742387, 4774238723871194, 47742387238711937387119361935597
10, 5, 53, 5277, 52767639, 5276763876383820,
52767638763838197638381938191910

seq (a(n,1), n=1..10);
1, 1, 6, 58, 5829, 58292915, 5829291479146458,
58292914791464577914645739573229,
5829291479146457791464573957322929146457395732288957322869786615,
58292914791464577914645739573229291464573957322889573228697866147914645739573228895732286978661464573228697866144478661434893308

With regards, Alois

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