A175578 Decimal expansion of the sum over the inverse icosahedral numbers.

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

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

G. C. Greubel, Table of n, a(n) for n = 1..10000

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 *)

Prog

(PARI) Euler+Pi*sqrt(5/3)*tanh(Pi*sqrt(15)/10)/2+real(psi(1/2+ I*sqrt(15)/10)) \\ Charles R Greathouse IV, Jul 19 2013

Crossrefs

Cf. A006564 (icosahedral numbers).

Cf. sums of inverses: A152623 (tetrahedral numbers), A002117 (cubes), A175577 (octahedral numbers), A295421 (dodecahedral numbers).

Sequence in context: A254105 A247548 A001600 * A347861 A316609 A307327

Adjacent sequences: A175575 A175576 A175577 * A175579 A175580 A175581

Keyword

cons,easy,nonn

Author

R. J. Mathar, Jul 15 2010

Status

approved