OFFSET
0,1
COMMENTS
Product of Artin's constant of rank 3 and the equivalent almost-prime products.
LINKS
Zak Seidov, Table of n, a(n) for n = 0..999
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 = 3.
s*Sum_{j=1..floor(s/4)} binomial(s-3j-1, j-1)/j = A014097(s)-1.
Equals 1/Product_{k=1..4} Gamma(1-x_k), where x_k are the 4 roots of the polynomial x*(x+1)^3-1. [R. J. Mathar, Feb 20 2009]
EXAMPLE
0.85067063079110435... = (1 - 1/8)*(1 - 1/54)*(1 - 1/192)*(1 - 1/500)*(1 - 1/1080)*...
MAPLE
r := 3 : ni := fsolve( (n+1)^r*n-1, n, complex) : 1.0/mul(GAMMA(1-d), d=ni) ; # R. J. Mathar, Feb 20 2009
MATHEMATICA
p[k_] := Gamma[1 - Root[#^4 + 3#^3 + 3#^2 + # - 1&, k]]; RealDigits[1/(p[1]*p[2]*p[3]*p[4]) // Re, 10, 105] // First (* Jean-François Alcover, Feb 11 2013, after R. J. Mathar *)
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Feb 13 2009
EXTENSIONS
Offset in b-file corrected by N. J. A. Sloane, Aug 31 2009
Data extended by Jean-François Alcover, Feb 11 2013
STATUS
approved