|
| |
|
|
A175578
|
|
Decimal expansion of the sum over the inverse icosahedral Numbers.
|
|
0
|
|
|
|
1, 1, 2, 3, 5, 6, 5, 9, 6, 6, 8, 9, 9, 2, 5, 1, 8, 8, 7, 5, 7, 3, 9, 3, 7, 5, 7, 9, 0, 1, 5, 8, 7, 9, 6, 4, 5, 3, 5, 3, 8, 1, 1, 4, 1, 6, 4, 8, 5, 5, 0, 4, 9, 8, 0, 6, 0, 6, 1, 7, 0, 2, 6, 9, 2, 9, 8, 1, 9, 2, 6, 0, 3, 3, 6, 1, 5, 4, 2, 6, 6, 9, 5, 8, 2, 6, 0, 9, 2, 1, 0, 6, 8, 8, 8, 7, 7, 8, 1, 0, 7, 2, 6, 4, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Defined by sum_{n>=1} 1/A006564(n) = 1/1 + 1/12 +1/48 + 1/124 +...
Equals gamma + Pi*sqrt(5/3)*tanh(Pi*sqrt(15)/10)/2 + Re psi( 1/2+i*sqrt(15)/10 ), where psi is the digamma function, i the imaginary unit, Pi = A000796, sqrt(15)=A010472, gamma=A001620.
|
|
|
LINKS
|
Table of n, a(n) for n=1..105.
|
|
|
EXAMPLE
|
1.12356596689925188757393..
|
|
|
MAPLE
|
Digits := 120 : gamma+ Psi(1/2+sqrt(15)*I/10)+sqrt(15)/6*Pi*tanh(Pi*sqrt(15)/10) ; evalf(Re(%)) ;
|
|
|
MATHEMATICA
|
N[EulerGamma + PolyGamma[1/2 + (I*Sqrt[15])/10] + (1/2)*Tanh[(Pi*Sqrt[15])/10]*Pi*Sqrt[5/3] // Re, 105] // RealDigits // First (* Jean-François Alcover, Feb 05 2013 *)
|
|
|
CROSSREFS
|
Sequence in context: A191741 A191665 A001600 * A000036 A165081 A165089
Adjacent sequences: A175575 A175576 A175577 * A175579 A175580 A175581
|
|
|
KEYWORD
|
cons,easy,nonn
|
|
|
AUTHOR
|
R. J. Mathar, Jul 15 2010
|
|
|
STATUS
|
approved
|
| |
|
|
