A121473 Partial quotients of the continued fraction expansion of the constant A121472 defined by the sums: c = Sum_{n>=1} 1/2^[log_2(e^n)] = Sum_{n>=1} [log(2^n)]/2^n.

0, 1, 6, 146, 8, 37783544111994270385152, 784637716923335095479473680436259502469253233551410733056, 309485009821345068724781056

Offset

0,3

Comments

A "devil's staircase" type of constant has large partial quotients in its continued fraction expansion. See MathWorld link for more information.

Links

Table of n, a(n) for n=0..7.

Eric Weisstein's World of Mathematics, Devil's Staircase

Example

c=0.857282383103406177511903308509733997590988312093146922257824...
The number of 1's in the binary expansion of a(n) is given by
the partial quotients of continued fraction of log(2):
log(2) = [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...]
as can be seen by the binary expansions of a(n):
a(0) = 0
a(1) = 2^0
a(2) = 2^2 + 2^1
a(3) = 2^7 + 2^4 + 2^1
a(4) = 2^3
a(5) = 2^75 + 2^62 + 2^49 + 2^36 + 2^23 + 2^10
a(6) = 2^189 + 2^101 + 2^13
a(7) = 2^88
a(8) = 2^277
a(9) = 2^1007 + 2^365
a(10) = 2^642
a(11) = 2^1649
a(12) = 2^2291
a(13) = 2^3940
a(14) = 2^26573 + 2^16402 + 2^6231

Crossrefs

Cf. A121472 (constant), A121474 (dual constant), A121475.

Sequence in context: A280847 A041271 A196964 * A166837 A166809 A250389

Adjacent sequences: A121470 A121471 A121472 * A121474 A121475 A121476

Keyword

cofr,nonn

Author

Paul D. Hanna, Aug 01 2006

Status

approved