The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=0..97. 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 Adjacent sequences: A072110 A072111 A072112 * A072114 A072115 A072116 KEYWORD base,cofr,easy,nonn,changed AUTHOR Benoit Cloitre, Jun 19 2002 EXTENSIONS Offset changed by Andrew Howroyd, Jul 06 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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