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Continued fraction expansion of the value of Minkowski's question mark function at the base of the natural logarithm.
(history; published version)
#5 by Russ Cox at Sun Jul 10 18:41:28 EDT 2011
LINKS

<a href="/Sindx_index/Me.html#MinkowskiQ">Index entries for Minkowski's question mark function</a>

<a href="/Sindx_index/Me.html#MinkowskiQ">Index entries for sequences related to Minkowski's question mark function</a>

Discussion
Sun Jul 10
18:41
OEIS Server: https://oeis.org/edit/global/58
#4 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010
LINKS

<a href="/Sindx_Me.html#MinkowskiQ">Index entries for Minkowski's question mark function</a>

<a href="/Sindx_Me.html#MinkowskiQ">Index entries for sequences related to Minkowski's question mark function</a>

KEYWORD

cofr,nonn,new

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009
LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_Me.html#MinkowskiQ">Index entries for Minkowski's question mark function</a>

<a href="http://www.research.att.com/~njas/sequences/Sindx_Me.html#MinkowskiQ">Index entries for sequences related to Minkowski's question mark function</a>

KEYWORD

cofr,nonn,new

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
CROSSREFS

Cf. 120026A120026.

KEYWORD

cofr,nonn,new

#1 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006
NAME

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

DATA

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

<a href="http://www.research.att.com/~njas/sequences/Sindx_Me.html#MinkowskiQ">Index entries for Minkowski's question mark function</a>

<a href="http://www.research.att.com/~njas/sequences/Sindx_Me.html#MinkowskiQ">Index entries for sequences related to Minkowski's question mark function</a>

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. 120026.

KEYWORD

cofr,nonn

AUTHOR

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

STATUS

approved