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A072113 Continued fraction expansion of Hall and Tenenbaum constant. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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 (decimal expansion).
Sequence in context: A365116 A132558 A358288 * A105433 A196086 A196083
KEYWORD
base,cofr,easy,nonn,changed
AUTHOR
Benoit Cloitre, Jun 19 2002
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 06 2024
STATUS
approved

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Last modified July 17 09:45 EDT 2024. Contains 374364 sequences. (Running on oeis4.)