A143304 - OEIS

%I #11 Aug 27 2020 04:19:14

%S 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,

%T 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,

%U 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

%N Decimal expansion of Norton's constant.

%C 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

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

%H Graham H. Norton, <a href="https://doi.org/10.1016/S0747-7171(08)80036-3">On the asymptotic analysis of the Euclidean algorithm</a>, J. Symbolic Comput., Vol. 10 (1990), pp. 53-58.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NortonsConstant.html">Norton's Constant</a>.

%F Equals -((Pi^2 - 6*log(2)*(-3 + 2*EulerGamma + log(2) + 24*log(Glaisher) - 2*log(Pi)))/Pi^2).

%F Equals (12*log(2)/Pi^2) * (zeta'(2)/zeta(2) - 1/2) + A086237 - 1/2. - _Amiram Eldar_, Aug 27 2020

%e 0.06535142592303732137...

%t 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 *)

%Y Cf. A001620, A074962, A086237, A306016.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Aug 05 2008