login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146481 Decimal expansion of Product_{n=2...infinity} (1-1/(n*(n-1))). 1
2, 9, 6, 6, 7, 5, 1, 3, 4, 7, 4, 3, 5, 9, 1, 0, 3, 4, 5, 7, 0, 1, 5, 5, 0, 2, 0, 2, 1, 9, 1, 4, 2, 8, 6, 4, 8, 6, 4, 8, 3, 1, 5, 1, 9, 1, 7, 8, 9, 4, 7, 8, 9, 0, 8, 1, 6, 7, 3, 5, 7, 3, 3, 1, 6, 5, 9, 0, 6, 1, 6, 2, 9, 1, 5, 1, 9, 6, 0, 8, 8, 8, 3, 6, 6, 7, 4, 8, 1, 6, 4, 0, 2, 1, 2, 6, 2, 2, 1, 4, 5, 4, 1, 7, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Product of Artin's constant A005596 and the equivalent almost-prime products.

LINKS

Table of n, a(n) for n=0..104.

M. Chamberland, A. Straub, On gamma constants and infinite products, arXiv:1309.3455

R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], first line Table 3.

FORMULA

The logarithm is -sum_{s>=2} sum_{j=1..floor[s/(1+r)]} binomial(s-r*j-1,j-1)*(1-Zeta(s))/j at r=1.

s*sum_{j=1..floor[s/2]} binomial(s-j-1,j-1)/j = A001610(s-1).

Equals 1/product_{k=1..2} Gamma(1-x_k) = -sin(A094886)/A000796, where x_k are the 2 roots of the polynomial x*(x+1)-1. [From R. J. Mathar, Feb 20 2009]

EXAMPLE

0.2966751347435910345.. = (1-1/2)*(1-1/6)*(1-1/12)*(1-1/20)*..

MAPLE

phi := (1+sqrt(5))/2; evalf(-sin(Pi*phi)/Pi) ; [From R. J. Mathar, Feb 20 2009]

MATHEMATICA

RealDigits[-Cos[Pi*Sqrt[5]/2]/Pi, 10, 105] // First (* Jean-François Alcover, Feb 11 2013 *)

CROSSREFS

Cf. A005596.

Sequence in context: A010598 A152564 A138029 * A233766 A021341 A011247

Adjacent sequences:  A146478 A146479 A146480 * A146482 A146483 A146484

KEYWORD

nonn,cons

AUTHOR

R. J. Mathar, Feb 13 2009

EXTENSIONS

More terms from Jean-François Alcover, Feb 11 2013

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified July 24 03:48 EDT 2017. Contains 289717 sequences.