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Continued fraction expansion of the value of Minkowski's question mark function at the base of the natural logarithm.
1

%I #5 Jul 10 2011 18:41:28

%S 2,1,4,2,2,1,1,6,2,4,1,1,1,4,1,1,2,14,2,3,2,1,1,2,2,2,1,1,8,1,2,1,1,2,

%T 2,1,3,2,11,979,3,19,1,1,39,2,1,4,4,4,1,27,1,1,22,6,1,8,13,1,1,1,24,5,

%U 3,21,8,3,1,2,1,2,2,1,2,1,1,2,4,1,6,1,2,1,1,12,77,2,1,4,2,4,2,1,2,1,35,2

%N Continued fraction expansion of the value of Minkowski's question mark function at the base of the natural logarithm.

%H <a href="/index/Me#MinkowskiQ">Index entries for Minkowski's question mark function</a>

%H <a href="/index/Me#MinkowskiQ">Index entries for sequences related to Minkowski's question mark function</a>

%F 2 + 2(Sum[(-1)^(k)/2^(1/9*k^2 + k - 1), {k, 3, n, 3}] + Sum[(-1)^(k)/2^((1/9)(k + 8)(k - 1)), {k, 4, n, 3}] + Sum[(-1)^(k)/2^((1/9)(k^2 + 5*k - 5)), {k, 2, n, 3}])

%t ContinuedFraction[(cf = ContinuedFraction[E, 150(*arbitrary precision*)]; IntegerPart[E] + Sum[(-1)^(k)/2^(Sum[cf[[i]], {i, 2, k}] - 1), {k, 2, Length[cf]}]), 100]

%Y Cf. A120026.

%K cofr,nonn

%O 0,1

%A Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 04 2006