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A175578 Decimal expansion of the sum over the inverse icosahedral numbers. 5
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

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-Fran├žois 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 * A316609 A000036 A165081

Adjacent sequences:  A175575 A175576 A175577 * A175579 A175580 A175581

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Jul 15 2010

STATUS

approved

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Last modified October 17 18:47 EDT 2018. Contains 316293 sequences. (Running on oeis4.)