[seqfan] Re: plastic number base

Charles Greathouse charles.greathouse at case.edu
Thu Jul 11 16:39:43 CEST 2013


Graeme, Allan, please add those sequences!

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Thu, Jul 11, 2013 at 2:27 AM, Graeme McRae <graememcrae at gmail.com> wrote:

> 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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> >
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> >
>
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