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
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
KEYWORD
cofr,nonn
AUTHOR
Paul D. Hanna, Aug 01 2006
STATUS
approved