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

Author

R. J. Mathar, Jul 15 2010

Keywords

• cons
• easy
• nonn

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.

Examples

			1.12356596689925188757393..
		

Links

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

Crossrefs

Cf. A006564 (icosahedral numbers).

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

Programs

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 *)

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