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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. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Added more terms, Joerg Arndt, Sep 09 2013

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)