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

1,2

Comments

Next term > 3*10^9.

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

Links

Table of n, a(n) for n=1..36.

H. Havermann, Simple Continued Fraction for Pi

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

Example

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

Crossrefs

Cf. A001203, A048613.

Sequence in context: A317850 A181828 A328980 * A091679 A116034 A364166

Adjacent sequences: A059098 A059099 A059100 * A059102 A059103 A059104

Keyword

cofr,nonn

Author

Hans Havermann, Feb 13 2001

Extensions

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

Status

approved