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A059101 Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A244334 A011398 A181828 * A091679 A116034 A122987

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

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Last modified August 19 01:29 EDT 2017. Contains 290787 sequences.