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 A072113 Continued fraction expansion of Hall and Tenenbaum constant. 1

%I #11 Jan 26 2015 03:43:26

%S 0,3,23,1,1,16,1,2,1,8,1,274,3,1,5,1,2,1,16,1,3,3,2,1,4,1,1,2,1,2,1,2,

%T 1,1,2,16,3,3,2,1,1,1,2,69,121,1,5,1,2,1,2,1,1,1,2,1,12,4,1,1,1,1,2,1,

%U 2,3,3,1,3,2,4,1,7,1,16,2,4,1,2,7,2,3,1,3,2,1,1,1,1,2,1,1,3,1,1,3,2,1

%N Continued fraction expansion of Hall and Tenenbaum constant.

%C For any multiplicative function g with values -1<= g(k) <= 1, for any real x >=2, Sum( i<= x, g(i) ) << x * exp{ -K * Sum( p<=x, (1-g(p))/p ) } and K is the optimal constant satisfying this inequality ( Hall and Tenenbaum, 1991).

%D G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, p. 348, Publications de l'Institut Cartan, 1990.

%F K = cos(S) = 0.3287... where S it the root 0< S < 2Pi of sin(S)+(Pi-S)*cos(S) = Pi/2.

%o (PARI) \p200;

%o contfrac(cos(solve(X=0,2*Pi,sin(X)+(Pi-X)*cos(X)-Pi/2)))

%Y Cf. A072112.

%K base,cofr,easy,nonn

%O 1,2

%A _Benoit Cloitre_, Jun 19 2002

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Last modified September 24 19:02 EDT 2023. Contains 365581 sequences. (Running on oeis4.)