Re: [math-fun] Ulam(1,2)

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).

I've now found such a set of length 251. To state it in another way, the first differences of these two sections of length 251 are the same.