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A317558 Number of decimal digits to which the n-th convergent of the continued fraction expansion of log(2) matches the correct value. 3
0, -1, 1, 0, 2, 4, 5, 4, 5, 6, 6, 6, 7, 8, 9, 10, 11, 10, 12, 13, 13, 13, 14, 15, 15, 16, 17, 18, 20, 22, 22, 23, 23, 24, 25, 26, 27, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 40, 39, 41, 39, 43, 44, 45, 46, 48, 48, 49, 51, 52, 52, 54, 54, 55, 55, 56, 57, 57, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Decimal expansion of log(2) in A002162.
For the number of correct binary digits see A317557.
For the similar case of number of correct decimal digits of Pi see A084407.
LINKS
FORMULA
Lim_{n -> oo} a(n)/n = 2*log(A086702)/log(10) = 2*A100199/log(10) = 2*A240995.
EXAMPLE
n convergent decimal expansion a(n)
== ============ ==================== ====
1 0 / 1 0.0 0
2 1 / 1 1.0 -1
3 2 / 3 0.66... 1
4 7 / 10 0.7... 0
5 9 / 13 0.692... 2
6 61 / 88 0.69318... 4
7 192 / 277 0.693140... 5
8 253 / 365 0.69315... 4
9 445 / 642 0.693146... 5
10 1143 / 1649 0.6931473... 6
oo lim = log(2) 0.693147180559945... --
MATHEMATICA
a[n_] := Block[{k = 1, a = RealDigits[Log@2, 10, n + 10][[1]], b = RealDigits[ FromContinuedFraction@ ContinuedFraction[ Log@2, n], 10, n + 10][[1]]}, While[a[[k]] == b[[k]], k++]; k - 1]; a[1] = 0; a[2] = -1; Array[a, 69] (* Robert G. Wilson v, Aug 09 2018 *)
CROSSREFS
Sequence in context: A317499 A004581 A212790 * A070784 A200289 A165044
KEYWORD
sign,base
AUTHOR
A.H.M. Smeets, Jul 31 2018
EXTENSIONS
a(61) onward from Robert G. Wilson v, Aug 09 2018
STATUS
approved

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Last modified October 1 02:41 EDT 2023. Contains 365812 sequences. (Running on oeis4.)