A228918 Alternating sum of inverse of increasing integers with a difference of 0, 1, 2, 3, ...: 1 - 1/2 + 1/4 - 1/7 + 1/11 - 1/16 + 1/22 - 1/29 + 1/37 + ... i.e., alternating series based on A226985.

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

Offset

0,1

Links

Table of n, a(n) for n=0..107.

Formula

See Mathematica program. - Joerg Arndt, Sep 09 2013

Example

0.66157019207358511204457389...

Maple

c:= Sum( (-1)^k/(1+binomial(k+1, 2)), k=0..infinity):
Re(evalf(c, 120));  # Alois P. Heinz, Sep 09 2013

Mathematica

N[((-2 I) (LerchPhi[-1, 1, 1/2 - (I/2) Sqrt[7]] - LerchPhi[-1, 1, 1/2 + (I/2) Sqrt[7]]))/Sqrt[7], 99] (* Joerg Arndt, Sep 09 2013 *)
-(2*Im[PolyGamma[(1-I*Sqrt[7])/4] - PolyGamma[(3-I*Sqrt[7])/4]])/Sqrt[7] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Sep 10 2013 *)

Prog

(PARI) default(realprecision, 133); sumalt(k=1, 1/(1+k*(k-1)/2)*(-1)^(k+1))
(PARI) -(2*imag(psi((1-I*sqrt(7))/4)-psi((3-I*sqrt(7))/4)))/sqrt(7) \\ sumalt is faster; Charles R Greathouse IV, Sep 10 2013

Crossrefs

Cf. A226985, A000124.

Sequence in context: A133890 A248059 A111719 * A200281 A199864 A153605

Adjacent sequences: A228915 A228916 A228917 * A228919 A228920 A228921

Keyword

nonn,cons

Author

Didier Guillet, Sep 08 2013

Extensions

More terms from Joerg Arndt, Sep 09 2013

Status

approved