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A175577 Decimal expansion of the sum of the reciprocals of the octahedral numbers (A005900). 5
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..105.

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

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

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Last modified February 20 04:27 EST 2018. Contains 299358 sequences. (Running on oeis4.)