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A121474 A devil's staircase constant: decimal expansion of the sums involving powers of 2 and Beatty sequences given by: c = Sum_{n>=1} [log_2(e^n)]/2^n = Sum_{n>=1} 1/2^[log(2^n)]. 3

%I

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

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

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

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

%C The continued fraction (A121475) of this constant has large partial quotients: c = [2; 3, 42, 4, 4512412933881984, ...]. See the MathWorld link for more information regarding devil's staircase constants. The dual constant is: A121472 = Sum_{n>=1} 1/2^[log_2(e^n)] = Sum_{n>=1} [log(2^n)]/2^n.

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

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

%e c=2.3307240704500978473572726401780935386031486101438756503210824331667...

%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

%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

%Y Cf. A121475 (continued fraction), A121472 (dual constant), A121473.

%K cons,nonn

%O 1,1

%A _Paul D. Hanna_, Aug 01 2006

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)