A120025 Continued fraction expansion of the value of Minkowski's question mark function at the base of the natural logarithm.

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..97.

Index entries for Minkowski's question mark function

Index entries for sequences related to Minkowski's question mark function

Formula

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}])

Mathematica

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]

Crossrefs

Cf. A120026.

Sequence in context: A145983 A245025 A257495 * A109090 A220780 A323915

Adjacent sequences: A120022 A120023 A120024 * A120026 A120027 A120028

Keyword

cofr,nonn

Author

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

Status

approved