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MAPLE
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[seq(frac2position_in_0_1_SB_tree(sqrt_n_confrac2binfrac(j)), j=1..40)];
sqrt_n_confrac2binfrac := proc(n) local c, t; c := CONFRACS_FOR_sqrt_N[n]; t := `if`((1 = nops(c)), [], `if`((0 = (nops(c) mod 2)), [op(c[2..nops(c)]), op(c[2..nops(c)])], c[2..nops(c)])); RETURN( (((2^c[1])-1) + `if`(1 = nops(c), 0, (runcounts2binexp0(t) / ((2^(convert(t, `+`)))-1)))) / (2^c[1])); end;
runcounts2binexp0 := proc(c) local i, e, n; n := 0; for i from 0 to nops(c)-1 do e := c[i+1]; n := ((2^e)*n) + ((i mod 2)*((2^e)-1)); od; RETURN(n); end;
CONFRACS_FOR_sqrt_N := [[1], [1, 2], [1, 1, 2], [2], [2, 4], [2, 2, 4], [2, 1, 1, 1, 4], [2, 1, 4], [3], [3, 6], etc., adapted from Weisstein's encyclopedia entry for Continued Fractions]
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