[seqfan] Re: Replacing chunks by their average

[Aai]

If I'm not wrong the numbers 14 on line 2 should be 1,4 and 1,4



Eric Angelini schreef op 28-03-15 om 20:27:
> S=
> 1,2,2,2,1,3,2,2,1,2,4,3,1,2,1,2,1,7,2,4,1,2,1,2,1,2,12,3,1,4,1,2,1,2,1,2,1,23,
> 2,4,1,4,1,2,1,2,1,2,1,2,44,3,14,14,1,2,1,2,1,2,1,2,1,87,2,4,1,4,1,4,1,2,1,2,1,
> 2,1,2,1,2,172,3,1,4,1,4,1,4,1,2,1,2,1,2,1,2,1,2,1,343,...
>
> Hello SeqFans,
> Replace in S all chunks of same-parity integers by the average of the said chunk and you will get S back.
>
> Example:
> - the first chunk is made by 1, -- replace it with 1;
> - the second chunk is 2,2,2, -- replace it with 2;
> - the third chunk is 1,3, -- replace it with 2;
> - the fourth chunk is 2,2, -- replace it with 2;
> - the fifth chunk is made by 1, -- replace it with 1;
> - the sixth chunk is made by 2,4, -- replace it by 3;
> etc.
> The replacements so far have been 1,2,2,2,3,1... which rebuilds S.
>
> ----
> In considering S, one quickly notices this array where the rightmost diagonal is A023105:
>
> 1,
> 2,
> 2,
> 2,1,3,
> 2,2,1,2,4,
> 3,1,2,1,2,1,7,
> 2,4,1,2,1,2,1,2,12,
> 3,1,4,1,2,1,2,1,2,1,23,
> 2,4,1,4,1,2,1,2,1,2,1,2,44,
> 3,14,14,1,2,1,2,1,2,1,2,1,87,
> 2,4,1,4,1,4,1,2,1,2,1,2,1,2,1,2,172,
> 3,1,4,1,4,1,4,1,2,1,2,1,2,1,2,1,2,1,343,
> ...
>
> Best,
> É.
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

-- 
Met vriendelijke groet,
@@i = Arie Groeneveld