|
Search: id:A146492
|
|
|
| A146492 |
|
Decimal expansion of Product_{n=2...infinity} (1-1/(n^4*(n-1))). |
|
+0
1
|
|
| 9, 2, 9, 8, 3, 8, 4, 7, 3, 9, 5, 4, 3, 4, 6, 8, 5, 2, 2, 3, 8, 3, 1, 8, 4, 6, 9, 5, 3, 4, 5, 5, 3, 5, 4, 8, 9, 4, 4, 9, 0, 8, 3, 0, 5, 4, 8, 2, 2, 5, 3, 6, 3, 5, 2, 3, 6
(list; cons; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Product of Artin's constant of rank 4 and the equivalent almost-prime products.
|
|
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=4.
s*sum_{j=1..floor[s/5]} binomial(s-4j-1,j-1)/j = A058368(s)-1.
Equals 1/product_{k=1..5} Gamma(1-x_k), where x_k are the 5 roots of the polynomial x*(x+1)^4-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
|
|
EXAMPLE
|
0.9298384739543468522383.. = (1-1/16)*(1-1/162)*(1-1/768)*(1-1/2500)*..
|
|
MAPLE
|
r := 4 : ni := fsolve( (n+1)^r*n-1, n, complex) : 1.0/mul(GAMMA(1-d), d=ni) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
|
|
CROSSREFS
|
Cf. A065416.
Sequence in context: A157215 A021919 A078127 this_sequence A090298 A094581 A040080
Adjacent sequences: A146489 A146490 A146491 this_sequence A146493 A146494 A146495
|
|
KEYWORD
|
nonn,cons
|
|
AUTHOR
|
R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2009
|
|
|
Search completed in 0.002 seconds
|
