A059101 - OEIS

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

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OFFSET

1,2

COMMENTS

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

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

LINKS

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

Hans 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

nonn

AUTHOR

Hans Havermann, Feb 13 2001

EXTENSIONS

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

STATUS

approved