In Lecture Notes on Enormous integers Harvey M. Friedman introduces
"... longest finite sequence $x_1,...,x_n$ from $\{1,...,k\}$ such that for no i < j <= n/2 is $x_i,...,x_{2i}$ a subsequence of $x_j,...,x_{2j}$. For k ≥ 1, let n(k) be the length of this longest finite sequence."
Then, the author evaluates this function
"Paul Sally runs a program for gifted high school students at the University of Chicago. He asked them to find n(1), n(2), n(3). They all got n(1) = 3. One got n(2) = 11. Nobody reported much on n(3)."
which I fail to confirm. Consider 12 character word
001011111101
neither of its starting subsequences
00 010 1011
is contained in "doubled" subsequences and suggest n(2) = 13. Am I missing anything?