[extropy-chat] Sequence

[Emlyn]

Ok, that was easy. Have a look at this, which is a bit more of the sequence:

0112 1223 1223 2334
1223 2334 2334 3445
1223 2334 2334 3445
2334 3445 3445 4556
1223 2334 2334 3445
2334 3445 3445 4556
2334 3445 3445 4556
3445 4556 4556 5667


Notice any interesting properties?

Here, I'll lay it out slightly differently:

0112 1223 1223 2334 1223 2334 2334 3445
1223 2334 2334 3445 2334 3445 3445 4556
1223 2334 2334 3445 2334 3445 3445 4556
2334 3445 3445 4556 3445 4556 4556 5667

-- 
Emlyn

http://emlynoregan.com   * blogs * music * software *


On Tue, 21 Sep 2004 10:05:15 -0700 (PDT), Adrian Tymes
<wingcat at pacbell.net> wrote:
> --- Emlyn <emlynoregan at gmail.com> wrote:
> > 01121223122323341223233423343445
> >
> > What comes next? Why?
> 
> This being a count of the number of 1s in the binary
> representation of each position number, the next set
> of numbers will (in binary) be the same numbers with a
> 1 in front, so just add 1 to each position:
> 
> 12232334233434452334344534454556
> 
> Or, more graphically:
> 
> 01121223122323341223233423343445
> 
> 01010101010101010101010101010101
> 00110011001100110011001100110011
> 00001111000011110000111100001111
> 00000000111111110000000011111111
> 00000000000000001111111111111111
> 00000000000000000000000000000000
> 
> 12232334233434452334344534454556
> 
> 01010101010101010101010101010101
> 00110011001100110011001100110011
> 00001111000011110000111100001111
> 00000000111111110000000011111111
> 00000000000000001111111111111111
> 11111111111111111111111111111111
> 
> 
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