A175577 Decimal expansion of the sum of the reciprocals of the octahedral numbers (A005900).

1, 2, 7, 8, 1, 8, 5, 1, 5, 9, 0, 9, 0, 9, 4, 6, 1, 7, 9, 5, 4, 0, 3, 9, 0, 9, 4, 8, 3, 6, 7, 5, 7, 1, 3, 3, 8, 4, 2, 3, 9, 0, 1, 5, 3, 6, 8, 5, 1, 4, 0, 2, 0, 2, 0, 1, 7, 0, 3, 4, 6, 3, 8, 0, 4, 1, 6, 5, 7, 9, 9, 9, 1, 8, 3, 0, 6, 2, 0, 8, 2, 4, 4, 1, 8, 3, 6, 3, 2, 4, 5, 2, 0, 5, 0, 0, 7, 9, 6, 2, 3, 0, 5, 3, 9

Offset

1,2

Comments

Defined by Sum_{n>=1} 1/A005900(n) = 1/1 + 1/6 + 1/19 + 1/44 + ...

Equals 3*(gamma + Re psi(i/sqrt 2) ) = 3* Re(A001620 + psi(i*A010503)) where psi(i*A010503) = -0.1511539... + i*2.3152942... is a digamma function and i the imaginary unit.

Links

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

Example

1.2781851590909461795403909483...

Maple

Digits := 120 : 3*(gamma+Psi(I/sqrt(2))); evalf(Re(%)) ;

Mathematica

RealDigits[ 3/2*(2*EulerGamma + Re[PolyGamma[0, 1 - I/Sqrt[2]] + PolyGamma[0, 1 + I/Sqrt[2]]]), 10, 105] // First (* Jean-François Alcover, Feb 11 2013 *)

Prog

(PARI) 3*Euler+3*real(psi(I/sqrt(2))) \\ Charles R Greathouse IV, Jul 19 2013
(PARI) sumnumrat(3/n/(2*n^2 + 1), 1) \\ Charles R Greathouse IV, Feb 08 2023

Crossrefs

Cf. A005900 (octahedral numbers).

Cf. sums of inverses: A152623 (tetrahedral numbers), A002117 (cubes), A295421 (dodecahedral numbers), A175578 (icosahedral numbers).

Sequence in context: A011416 A086658 A272182 * A189039 A198815 A011053

Adjacent sequences: A175574 A175575 A175576 * A175578 A175579 A175580

Keyword

cons,easy,nonn

Author

R. J. Mathar, Jul 15 2010

Status

approved