That's neat. It's very much like the Knuth -yllion naming system that uses a basis of 10, 10^2, 10^4, 10-^8, 10^16, etc. http://mrob.com/pub/math/largenum-2.html#yllion I wonder if you can devise a system that makes use of representations like "132" to shorten the typical length of representations. I naively suggest that 1 be left out whenever it leaves a descending pair of digits. You can also leave off the initial 1 if it is followed by another digit (which is always a 2 or more). Then you would count: 1, 2, 21, 3, 31, 32, 321, 23, 231, 232, 2321, 213, 2131, 2132, 21321, 4, 41, 42, ... On Sat, Dec 4, 2010 at 12:14, Steve Witham <sw@tiac.net> wrote:

Sometimes people describe 10^9 as a "thousand million" and use "billion" to refer to 10^12. [...]

Here is a minimal system starting with base two. Counting: 1, 12, 121, 13, 131, 1312, 13121, 123, 1231, 12312, 123121, 1213, 12131, 121312, 1213121, 14... The number 123 (eight) is analogous to "one thousand million"-- the first with two power numbers in a row. [...]

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