%I #6 Mar 30 2012 17:30:55
%S 0,1,2,5,7,33,106,563,1232,1795,8412,18619,27031,153774,6793087,
%T 6946861,34580531,41527392,117635315,512068652,629703967,1141772619,
%U 1771476586,9999155549,141759654272,151758809821,7729700145322,116097260989651
%N Numerators of convergents to Thue-Morse constant.
%F In continued fraction form, the Thue-Morse constant .4124540336401...; is [2, 2, 2, 1, 4, 3, 5, 2, 1, 4...], with A014572(1) = 2, the first partial quotient. Underneath each term we write the convergents corresponding to the continued fraction: [2] = 1/2, [2, 2] = 2/5, [2, 2, 2] = 5/12 and so on, the convergents being: 1/2, 2/5, 5/12, 7/17, 33/80, 106/257, 563/1365, 1232/2987, 1795/4352, 8412/20395...where the latter = .412454032...
%e [2,2,2,1,4] = 33/80 = .4125
%t mt = 0; Do[ mt = ToString[mt] <> ToString[(10^(2^n) - 1)/9 - ToExpression[mt]], {n, 0, 7}]; d = RealDigits[ N[ ToExpression[mt], 2^7]][[1]]; a = 0; Do[ a = a + N[ d[[n]]/2^(n + 1), 100], {n, 1, 2^7}]; f[n_] := FromContinuedFraction[ ContinuedFraction[a, n]]; Table[ Numerator[f[n]], {n, 1, 28}]
%Y Cf. A014571, A014572, A085395 (companion denominators).
%K frac,nonn
%O 1,3
%A _Gary W. Adamson_, Jun 27 2003
%E Edited by _Robert G. Wilson v_, Jul 15 2003