[seqfan] Re: A080605 Golomb seq samples extra 23

[Benoit Cloitre]

Thanks for catching this. Indeed there was a "paste" problem. Here my pari code 

 a=[1,3,3,3];for(n=3,20,for(i=1,a[n],a=concat(a,2*n-1)));a

giving

1, 
3, 3, 3, 5, 5, 5, 7, 7, 7,
9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 
15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 
21, 21, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 27, 27, 27, 27, 29, 29, 29, 29, 29, 29, 29, 29, 29,
31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39,...

Also my comment A080605(n)=tau^(2-tau)*(2n)^(tau-1)+O(1) is wrong since Vardy method gives  O(n^(tau-1)/log(n)) instead of O(1).

BC


Le 31 mai 2012 à 00:45, Kevin Ryde a écrit :

> In A080605 an odd numbers Golomb sequence, ie. its own run lengths of
> odd numbers, there might be a stray extra 23 in the sample values
> 
>     1,
>     3,  3,  3,                               <- 3 of
>     5,  5,  5,
>     7,  7,  7,
>     9,  9,  9,  9,  9,                       <- 5 of
>    11, 11, 11, 11, 11,
>    13, 13, 13, 13, 13,
>    15, 15, 15, 15, 15, 15, 15,               <- 7 of
>    17, 17, 17, 17, 17, 17, 17,   
>    19, 19, 19, 19, 19, 19, 19,
>    21, 21, 21, 21, 21, 21, 21, 21, 21,       <- 9 of
>    23, 23, 23, 23, 23, 23, 23, 23, 23, 23,   <- 10 of
>    25, 25, 25, 25, 25, 25, 25, 25, 25
> 
> At that 23s stage it would be a block of 9 many 23s would it, not 10?
> 
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