A121473 - OEIS

%I #5 Mar 30 2012 18:36:58

%S 0,1,6,146,8,37783544111994270385152,

%T 784637716923335095479473680436259502469253233551410733056,

%U 309485009821345068724781056

%N 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.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DevilsStaircase.html">Devil's Staircase</a>

%e c=0.857282383103406177511903308509733997590988312093146922257824...

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

%e the partial quotients of continued fraction of log(2):

%e log(2) = [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...]

%e as can be seen by the binary expansions of a(n):

%e a(0) = 0

%e a(1) = 2^0

%e a(2) = 2^2 + 2^1

%e a(3) = 2^7 + 2^4 + 2^1

%e a(4) = 2^3

%e a(5) = 2^75 + 2^62 + 2^49 + 2^36 + 2^23 + 2^10

%e a(6) = 2^189 + 2^101 + 2^13

%e a(7) = 2^88

%e a(8) = 2^277

%e a(9) = 2^1007 + 2^365

%e a(10) = 2^642

%e a(11) = 2^1649

%e a(12) = 2^2291

%e a(13) = 2^3940

%e a(14) = 2^26573 + 2^16402 + 2^6231

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

%K cofr,nonn

%O 0,3

%A _Paul D. Hanna_, Aug 01 2006