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A274031
Decimal expansion of a doubly infinite sum involving harmonic numbers. Curiously, this sum is very close to 1.
0
9, 9, 9, 2, 2, 2, 8, 3, 7, 7, 6, 3, 8, 3, 0, 0, 0, 8, 7, 6, 1, 9, 3, 5, 7, 4, 9, 2, 4, 7, 5, 6, 9, 8, 8, 6, 0, 3, 6, 9, 9, 5, 5, 1, 6, 1, 3, 6, 1, 7, 0, 9, 4, 4, 2, 0, 4, 8, 9, 8, 4, 3, 5, 8, 6, 2, 7, 6, 1, 0, 2, 2, 9, 7, 3, 5, 5, 0, 1, 2, 4, 2, 2, 2, 1, 9, 6, 3, 5, 3, 5, 0, 3, 5, 5, 9, 7, 6, 4, 7, 3, 9, 2
OFFSET
0,1
LINKS
R. Pemantle, C. Schneider, When is 0.999... equal to 1?, arXiv:math/0511574 [math.CO], 2005.
FORMULA
Sum_{j >= 1, k >= 1} H(j) (H(k+1)-1)/(j k (k+1) (j+k)), where H(j) is the j-th harmonic number.
Equals -4 zeta(2) - 2 zeta(3) + 4 zeta(2) zeta(3) + 2 zeta(5).
EXAMPLE
0.99922283776383000876193574924756988603699551613617094420489843586276...
MATHEMATICA
RealDigits[-4 Zeta[2] - 2 Zeta[3] + 4 Zeta[2] Zeta[3] + 2 Zeta[5], 10,
103][[1]]
CROSSREFS
Sequence in context: A346929 A346927 A197149 * A111623 A229985 A019897
KEYWORD
nonn,cons
AUTHOR
STATUS
approved