Re: [math-fun] Hereditary Representation with 2's

Eric Angelini wrote:

which integers -- using only the digit '2' -- have an hereditary representation using only 2's? (no 1's allowed)? Integer 2 is a hit, of course, but what about 22, 222, 2222, 222222 etc.? http://mathworld.wolfram.com/HereditaryRepresentation.html

Let's see: 22 = 2^(2^2) + 2^2 + 2, so that works. Next: 222 = 2^(2^2 + 2 + 1) + 2^(2^2 + 2) + 2^(2^2) + 2^(2+1) + 2^2 + 2, so that doesn't work. In fact, no longer string of 2s will work either. Since they all end in 2222 and are thus congruent to 14 mod 16, their hereditary representations all end with ... + 2^(2+1) + 2^2 + 2. -- Fred W. Helenius fredh@ix.netcom.com