A121472 - OEIS

%I #7 Jun 13 2015 11:06:46

%S 8,5,7,2,8,2,3,8,3,1,0,3,4,0,6,1,7,7,5,1,1,9,0,3,3,0,8,5,0,9,7,3,3,9,

%T 9,7,5,9,0,9,8,8,3,1,2,0,9,3,1,4,6,9,2,2,2,5,7,8,2,4,2,9,2,4,6,0,6,9,

%U 3,3,3,3,2,6,8,3,3,6,3,4,8,2,8,9,1,0,8,1,1,5,2,4,9,3,5,4,1,1,2,7,0,0,6,2

%N A devil's staircase constant: decimal expansion of the sums involving powers of 2 and Beatty sequences given by: c = Sum_{n>=1} 1/2^[log_2(e^n)] = Sum_{n>=1} [log(2^n)]/2^n.

%C The continued fraction (A121473) of this constant has large partial quotients: c = [0; 1, 6, 146, 8, 37783544111994270385152, ...]. See the MathWorld link for more information regarding devil's staircase constants.

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

%F c = Sum_{n>=1} 1/2^[n/log(2)] = Sum_{n>=1} [n*log(2)]/2^n, where [z]=floor(z).

%e c=0.85728238310340617751190330850973399759098831209314692225782429246...

%o (PARI) a(n)=local(t=log(2),x=sum(m=1,10*(n+1),1/2^floor(m/t)));floor(10^n*x)%10

%o (PARI) a(n)=local(t=log(2),x=sum(m=1,10*(n+1),floor(m*t)/2^m));floor(10^n*x)%10

%Y Cf. A121473 (continued fraction), A121474 (dual constant), A121475.

%K cons,nonn

%O 0,1

%A _Paul D. Hanna_, Aug 01 2006