This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1) = 0 since there exists no odd number whose msa is 1; a(2) = 1 since there is only one odd number, 5 with k=2 2k+1, with k less than 2^2 whose msa is 2; a(3) = 0 since there exists no odd number whose msa is 3; a(4) = 1 since there is only one number, 1, less than 2^(4+1) whose msa is 4; a(5) = 2 since there are two numbers, 11 & 23, less than 2^(4+1) whose msa is 4; etc.
msa[n_] := If[ OddQ@ n, (3n + 1)/2, n/2]; f[n_] := Block[{k = 2n + 1}, Length@ NestWhileList[ msa@# &, k, # >= k &] - 1]; g[n_] := Length@ Select[ Range[ 2^(n - 1)], f@# == n &]; Array[ g, 20]
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