Re: [math-fun] new math

="Veit Elser" <ve10@cornell.edu>

Here's a puzzle I made up. In the 1960's it might have been used to get kids interested in "new math".

Find two infinite sequences of non-negative integers

a0, a1, a2, ... b0, b1, b2, ...

such that a0 = b0 = 0, and every non-negative integer can be uniquely expressed as the sum of two integers, one from each sequence.

Veit

One of my favorites, the Moser-de Bruijn sequence, 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, 85, 256, 257,... http://www.research.att.com/~njas/sequences/A000695, for A, and twice that for B, satisfy this. Of course countless variants can be derived from this. Perhaps I was traumatized by early exposure to "new math"?