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

Author

R. J. Mathar, Jul 15 2010

Keywords

• cons
• easy
• nonn

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.

Examples

			1.2781851590909461795403909483...
		

Links

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

Crossrefs

Cf. A005900 (octahedral numbers).

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

Programs

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 *)

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