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 A317558 #14 Aug 11 2018 20:56:20
%S A317558 0,-1,1,0,2,4,5,4,5,6,6,6,7,8,9,10,11,10,12,13,13,13,14,15,15,16,17,
%T A317558 18,20,22,22,23,23,24,25,26,27,27,28,29,31,32,33,34,35,36,38,40,39,41,
%U A317558 39,43,44,45,46,48,48,49,51,52,52,54,54,55,55,56,57,57,58
%N A317558 Number of decimal digits to which the n-th convergent of the continued fraction expansion of log(2) matches the correct value.
%C A317558 Decimal expansion of log(2) in A002162.
%C A317558 For the number of correct binary digits see A317557.
%C A317558 For the similar case of number of correct decimal digits of Pi see A084407.
%H A317558 A.H.M. Smeets, <a href="/A317558/b317558.txt">Table of n, a(n) for n = 1..20000</a>
%F A317558 Lim_{n -> oo} a(n)/n = 2*log(A086702)/log(10) = 2*A100199/log(10) = 2*A240995.
%e A317558 n convergent decimal expansion a(n)
%e A317558 == ============ ==================== ====
%e A317558 1 0 / 1 0.0 0
%e A317558 2 1 / 1 1.0 -1
%e A317558 3 2 / 3 0.66... 1
%e A317558 4 7 / 10 0.7... 0
%e A317558 5 9 / 13 0.692... 2
%e A317558 6 61 / 88 0.69318... 4
%e A317558 7 192 / 277 0.693140... 5
%e A317558 8 253 / 365 0.69315... 4
%e A317558 9 445 / 642 0.693146... 5
%e A317558 10 1143 / 1649 0.6931473... 6
%e A317558 oo lim = log(2) 0.693147180559945... --
%t A317558 a[n_] := Block[{k = 1, a = RealDigits[Log@2, 10, n + 10][[1]], b = RealDigits[ FromContinuedFraction@ ContinuedFraction[ Log@2, n], 10, n + 10][[1]]}, While[a[[k]] == b[[k]], k++]; k - 1]; a[1] = 0; a[2] = -1; Array[a, 69] (* _Robert G. Wilson v_, Aug 09 2018 *)
%Y A317558 Cf. A002162, A016730, A086702, A100199, A240995, A317557.
%K A317558 sign,base
%O A317558 1,5
%A A317558 _A.H.M. Smeets_, Jul 31 2018
%E A317558 a(61) onward from _Robert G. Wilson v_, Aug 09 2018