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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. 3
0, 1, 6, 146, 8, 37783544111994270385152, 784637716923335095479473680436259502469253233551410733056, 309485009821345068724781056 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 21:47 EDT 2021. Contains 346273 sequences. (Running on oeis4.)