[seqfan] Re: plastic number base

[Graeme McRae]

Allan, my computer-calculated numbers agree with your hand-calculated ones.
 Here's my table, up to 22
01 = ..........X|..................
02 = ........X..|....X.............
03 = .......X...|.X.....X..........
04 = ......X....|X.....X.....X.....
05 = .....X.....|X.....X.....X.....
06 = ....X......|.X..........X.....
07 = ....X....X.|....X.......X.....
08 = ...X.......|X.......X........X
09 = ...X....X..|........X........X
10 = ..X........|..X.....X........X
11 = ..X......X.|.....X...........X
12 = ..X....X...|.....X...........X
13 = .X.........|..X..............X
14 = .X.......X.|.......X.........X
15 = .X.....X...|.......X.........X
16 = .X....X....|...X........X....X
17 = X..........|...X........X....X
18 = X........X.|............X....X
19 = X......X...|............X....X
20 = X.....X....|....X.......X....X
21 = X....X.....|....X.......X....X
22 = X....X....X|....X.......X....X

Another interesting sequence, which doesn't seem to be in OEIS, is a(n) =
the smallest number that requires n 1's in base-plastic notation.  This
sequence is

1, 2, 3, 4, 16, 22, 29, 44, 116, 206, 325, 483, 1335, 1336, 2438, 3113,
3479, 10269, ...

As an example, a(5)=16 because 16 is the smallest number that requires 5
1's in base-plastic notation.

--Graeme McRae
Palmdale, CA


On Wed, Jul 10, 2013 at 1:32 PM, Allan Wechsler <acwacw at gmail.com> wrote:

>  1 = 1.
>  2 = 100.00001
>  3 = 1000.01000001
>  4 = 10000.1000001000001
>  5 = 100000.1000001000001
>  6 = 1000000.0100000000001
>  7 = 1000010.0000100000001
>  8 = 10000000.100000001000000001
>  9 = 10000100.000000001000000001
> 10 = 100000000.001000001000000001
>
> Number of 1's in canonical representation: [1, 2, 3, 4, 4, 3, 4, 4, 4, 4],
> assuming that my hand calculations are accurate.  This sequence is not in
> OEIS.
>
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