"David Wilson" <davidwwilson@attbi.com> wrote:
I took a look at Ulam(1,2), the Ulam sequence starting with (1, 2) and including every subsequent number which is a unique sum of distinct earlier terms. This is Sloane's A002858.
... Can anyone confirm my data?
Did you intend to use zero-based indexing? If u(0)=1, u(1)=2, I concur that u(1000)=12336, u(1999)=25511. Otherwise one of us has a bug. I also get u(10000)=132790, u(50000)=676043, u(74084)=1000002. But there's a pretty definite bug in the histogram. My histogram of f(n)=(u(n) mod 21.6)/21.6 agrees with yours in its general trend, but differs in particulars. For f(1000...1999) in 20 buckets I get 113 101 119 98 87 70 58 40 31 8 5 0 0 2 4 14 22 64 66 98 rather than your 110 101 120 97 90 67 58 40 31 9 4 0 0 2 7 11 22 64 66 101. As a test, I find that the five numbers in the [.5,.55) bucket arise from u(1091)=13533 (f=0.527771) u(1210)=14894 (f=0.53704834) u(1730)=21870 (f=0.5) u(1748)=22151 (f=0.50927734) u(1947)=24851 (f=0.50927734). What four numbers do you have? I agree exactly with Klaus Brockhaus's data for f(1000...1259), so I think I'm slightly likelier to be correct, but only slightly, and I'm pretty suspicious about the zero-based indexing. My data suggests that 21.6 should be about 21.60157 . Dan