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.
%I A085395 #10 Feb 06 2022 10:07:13
%S A085395 1,2,5,12,17,80,257,1365,2987,4352,20395,45142,65537,372827,16469925,
%T A085395 16842752,83840933,100683685,285208303,1241516897,1526725200,
%U A085395 2768242097,4294967297,24243078582,343698067445,367941146027,18740755368795
%N A085395 Denominators of convergents to the Thue-Morse constant 0.41245403364...
%F A085395 Write the convergents directly underneath the partial quotients (A014572) for 0.412454033... starting with the first partial quotient, 2: [2, 2, 2, 1, 4, 3, 5, 2, 1, 4, ...] such that [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, ...
%e A085395 [2, 2, 2, 1, 4] = 33/80 = 0.4125.
%t A085395 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[ Denominator[f[n]], {n, 1, 28}]
%Y A085395 Companion numerators are A085394.
%Y A085395 Cf. A085394, A014572, A014571.
%K A085395 frac,nonn
%O A085395 1,2
%A A085395 _Gary W. Adamson_, Jun 27 2003
%E A085395 Edited by _Robert G. Wilson v_, Jul 15 2003