A072113 Continued fraction expansion of Hall and Tenenbaum constant.

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, 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, 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

Offset

1,2

Comments

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).

References

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

Links

Table of n, a(n) for n=1..98.

Formula

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

Prog

(PARI) \p200;
contfrac(cos(solve(X=0, 2*Pi, sin(X)+(Pi-X)*cos(X)-Pi/2)))

Crossrefs

Cf. A072112.

Sequence in context: A232016 A132558 A358288 * A105433 A196086 A196083

Adjacent sequences: A072110 A072111 A072112 * A072114 A072115 A072116

Keyword

base,cofr,easy,nonn

Author

Benoit Cloitre, Jun 19 2002

Status

approved