A143304 Decimal expansion of Norton's constant.

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

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: A349249 A225665 A019686 * A021157 A242494 A357107

Adjacent sequences: A143301 A143302 A143303 * A143305 A143306 A143307

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 05 2008

Status

approved