A059101 Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant.

1, 3, 7, 8, 9, 10, 11, 15, 16, 17, 97, 100, 103, 117, 976, 32307, 32760, 32787, 60508, 60601, 60663, 187154, 230084, 1120375, 1146529, 2211732, 4497058, 1434927965, 1434935064, 1434935232, 1434935281, 1471575921, 1471636101, 1490844937, 1491643951, 1498931686

Offset: 1

Author

Hans Havermann, Feb 13 2001

Keywords

• nonn

Comments

Next term > 3*10^10. - Hans Havermann, Jul 29 2024

The geometric mean of 1498931686 terms is Khinchin + 1.00240496*10^-13.

Examples

			The geometric mean of 17 terms (Khinchin + 0.00752006) is not bettered until we calculate the geometric mean of 97 terms (Khinchin - 0.00326655).
		

Links

• Hans Havermann, Simple Continued Fraction for Pi

Crossrefs

Cf. A001203, A048613.

Formula

p = Rest[{A001203}]; q = N[1, 100]; r = p[[1]] + 1; t = {}; Do[q = q*p[[i]]; g = q^(1/i) - Khinchin; If[Abs[g] < r, r = Abs[g]; t = Append[t, i]], {i, 1, Length[p]}]; t

Extensions

a(28)-a(36) from Hans Havermann, Dec 27 2012