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A143304 Decimal expansion of Norton's constant. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 157.

LINKS

Table of n, a(n) for n=0..104.

Graham H. Norton, On the asymptotic analysis of the Euclidean algorithm, J. Symbolic Comput., Vol. 10 (1990), pp. 53-58.

Eric Weisstein's World of Mathematics, Norton's Constant.

FORMULA

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

EXAMPLE

0.06535142592303732137...

MATHEMATICA

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 *)

CROSSREFS

Cf. A001620, A074962, A086237, A306016.

Sequence in context: A225664 A225665 A019686 * A021157 A242494 A193211

Adjacent sequences:  A143301 A143302 A143303 * A143305 A143306 A143307

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Aug 05 2008

STATUS

approved

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Last modified February 26 22:53 EST 2021. Contains 341643 sequences. (Running on oeis4.)