At 06:55 PM 2/14/2003, Klaus Brockhaus wrote:

Using David Wilson's idea and Jud McCranie's data, I made some 216x246 gif-files (attached) which illustrate the observed phenomenon.

I don't know if this is known (or interesting or significant), but there are many "pseudo-repetitions" in the Ulam sequence. By this I mean a relatively large number, n, so that U(s+i+p)=(s+i)+d for i=0 .. n-1, for some constants s, p, and d. For instance

n=134
d=4131173

The 134 Ulam numbers starting with 51497 (Ulam number, not index) and the 134 Ulam numbers starting at 4182670 each differ by 4131173 (the corresponding terms, that is).