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A156019 Numerators in an infinite sum for Pi. 2
3, 15, 73, 1, 2, 3, 7, 1, 2, 2, 1, 2, 1, 3, 1, 2, 6, 1, 1, 3, 1, 6, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 2, 6, 1, 2, 3, 1, 1, 1, 45, 22, 2, 1, 1, 24, 2, 1, 2, 1, 2, 4, 2, 8, 5, 1, 1, 1, 2, 7, 1, 3, 1, 7, 4, 7, 3, 3, 9, 9, 1, 18, 3, 15, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For k >= 0, define Q(k) = A002485(2k)/A002486(2k) (convergents to Pi that are less than Pi), so Pi = Sum_{k>=1} (Q(k) - Q(k-1)). Then a(n) is the numerator of Q(n) - Q(n-1).
LINKS
FORMULA
a(n) = numerator(A002485(2n)/A002486(2n) - A002485(2n-2)/A002486(2n-2)).
EXAMPLE
a(2) = 15 since A002485(4)/A002486(4) = 333/106, A002485(2)/A002486(2) = 3/1, and 333/106 - 3/1 = 15/106 (see table below).
Pi = 3/1 + 15/106 + 73/877203 + 1/2195225334 + 2/17599271777 + 3/360950005720 + 7/17348726394920 + ....
.
n Q(n) = A002485(2n)/A002486(2n) Q(n) - Q(n-1) a(n)
- ------------------------------ ------------- ----
0 0/1 = 0 - -
1 3/1 = 3 3/1 3
2 333/106 = 3.1415094339... 15/106 15
3 103993/33102 = 3.1415926530... 73/877203 73
CROSSREFS
Cf. A000796, A002485, A002486, A156020 (denominators).
Sequence in context: A290902 A155117 A137638 * A145839 A232289 A055837
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
More terms from Alexander R. Povolotsky, Sep 01 2009
Edited by Jon E. Schoenfield, Jan 04 2022
More terms from Jinyuan Wang, Jun 29 2022
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)