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Search: id:A126389
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| A126389 |
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Numerators in a series for the "alternating Euler constant" ln(4/Pi). |
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+0
2
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| 1, -1, 2, -2, -1, 1, 1, -1, 1, -1, 3, -3, -2, 2, 2, -2, 2, -2, 2, -2, 4, -4, -3, 3, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 3, -3, -1, 1, 1, -1, 1, -1, 3, -3, 1, -1, 3, -3, 3, -3, 5, -5, -4, 4, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 4, -4, -2, 2
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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Nonzero values of (-1)^n*b(floor(n/2)) for n > 1, where b(n) = (# of 1's) - (# of 0's) in the base 2 expansion of n. The denominators of the series are A126388.
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REFERENCES
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J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
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LINKS
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J. Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi)
Eric Weisstein's MathWorld, Digit Count
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FORMULA
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ln(4/Pi) = 1/2 - 1/3 + 2/6 - 2/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 3/14 - 3/15 - 2/16 + 2/17 + 2/22 - ...
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EXAMPLE
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floor(15/2) = 7 = 111 base 2, which has (# of 1's) - (# of 0's) =
3, so (-1)^15*3 = -3 is a term.
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MATHEMATICA
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b[n_] := DigitCount[n, 2, 1] - DigitCount[n, 2, 0]; L = {}; Do[If[b[Floor[n/2]] != 0, L = Append[L, (-1)^n*b[Floor[n/2]]]], {n, 2, 100}]; L
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CROSSREFS
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Cf. A037861, A066879, A094640, A094641, A110625, A110626, A126388.
Sequence in context: A118164 A099563 A099564 this_sequence A105551 A073772 A164562
Adjacent sequences: A126386 A126387 A126388 this_sequence A126390 A126391 A126392
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KEYWORD
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base,sign
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 01 2007
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