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A143304
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Decimal expansion of Norton's constant.
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1
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0, 6, 5, 3, 5, 1, 4, 2, 5, 9, 2, 3, 0, 3, 7, 3, 2, 1, 3, 7, 8, 7, 8, 2, 6, 2, 6, 7, 6, 3, 1, 0, 7, 9, 3, 0, 8, 1, 3, 0, 2, 4, 5, 3, 6, 8, 4, 9, 4, 2, 3, 7, 9, 7, 6, 5, 9, 0, 7, 1, 4, 4, 9, 6, 8, 1, 5, 7, 7, 0, 7, 5, 8, 0, 5, 4, 3, 1, 9, 9, 4, 9, 4, 6, 9, 4, 2, 0, 6, 8, 7, 1, 6, 3, 6, 4, 5, 5, 8, 9, 9, 7, 4, 2, 3
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OFFSET
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0,2
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COMMENTS
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The average number of divisions required by the Euclidean algorithm, for a pair of independently and uniformly chosen numbers in the range [1, N] is (12*log(2)/Pi^2) * log(N) + c + O(N^(e-1/6)), for any e>0, where c is this constant (Norton, 1990). - Amiram Eldar, Aug 27 2020
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 157.
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LINKS
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FORMULA
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Equals -((Pi^2 - 6*log(2)*(-3 + 2*EulerGamma + log(2) + 24*log(Glaisher) - 2*log(Pi)))/Pi^2).
Equals (12*log(2)/Pi^2) * (zeta'(2)/zeta(2) - 1/2) + A086237 - 1/2. - Amiram Eldar, Aug 27 2020
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EXAMPLE
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0.06535142592303732137...
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MATHEMATICA
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RealDigits[-((Pi^2 - 6*Log[2]*(24 * Log[Glaisher] + 2*EulerGamma + Log[2] - 2 * Log[Pi] - 3))/Pi^2), 10, 100][[1]] (* Amiram Eldar, Aug 27 2020 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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