login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121475 Partial quotients of the continued fraction expansion of the constant A121474 defined by the sums: c = Sum_{n>=1} [log_2(e^n)]/2^n = Sum_{n>=1} 1/2^[log(2^n)]. 3
2, 3, 42, 4, 4512412933881984, 2722258935367507708887588480171556995584, 2305843009213693952, 6277101735386680763835789423207666416102355444464034512896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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=2.330724070450097847357272640178093538603148610143875650321...

The number of 1's in the binary expansion of a(n) is given by

the partial quotients of continued fraction of 1/log(2):

1/log(2) = [1; 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, 1, ...]

as can be seen by the binary expansion of a(n):

a(0) = 2^1

a(1) = 2^1 + 2^0

a(2) = 2^5 + 2^3 + 2^1

a(3) = 2^2

a(4) = 2^52 + 2^43 + 2^34 + 2^25 + 2^16 + 2^7

a(5) = 2^131 + 2^70 + 2^9

a(6) = 2^61

a(7) = 2^192

a(8) = 2^698 + 2^253

a(9) = 2^445

a(10) = 2^1143

a(11) = 2^1588

a(12) = 2^2731

a(13) = 2^18419 + 2^11369 + 2^4319

CROSSREFS

Cf. A121474 (decimal expansion), A121472 (dual constant), A121473.

Sequence in context: A123993 A271331 A101821 * A334533 A196874 A087571

Adjacent sequences:  A121472 A121473 A121474 * A121476 A121477 A121478

KEYWORD

cofr,nonn

AUTHOR

Paul D. Hanna, Aug 01 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 27 13:36 EDT 2021. Contains 346306 sequences. (Running on oeis4.)