representation in base "triangle"

[Andrew Plewe]

While out getting food last night (Chanos in Los Angeles, highly
recommended), I came up with this "base" representation that varies a bit
from the normal form for a base.  I call it base "triangle" because you add
digits at successive triangle numbers.  Here are the integers 1 through 15
in base "triangle":

1      = 1
2      = 2
21     = 3
22     = 4
32     = 5
321    = 6
322    = 7
332    = 8
432    = 9
4321   = 10
4322   = 11
4332   = 12
4432   = 13
5432   = 14
54321  = 15

FYI, this was derived as follows.  Start with the value you'd like to
represent, we'll use 6, written out as a group of ones:

1 1 1 1 1 1

iteratively redistribute the leftmost value, adding 1 to each value to its
right:

  2 1 1 1 1
    2 2 1 1
      3 2 1

You stop when the leftmost value is greater than the number of values to its
right.

Not sure how useful this may be, but if anyone's seen it before or can rig
up a simple "base conversion" algorithm, let me know.  I'll add it to the
OEIS soon.

	-Andrew Plewe-