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A084407
Number of decimal places to which the n-th convergent of continued fraction expansion of Pi matches with the correct value.
10
0, 2, 4, 6, 9, 9, 9, 9, 11, 10, 12, 12, 14, 15, 15, 16, 17, 17, 18, 19, 21, 23, 24, 24, 25, 27, 29, 30, 30, 32, 33, 34, 37, 39, 40, 40, 41, 42, 44, 45, 45, 46, 47, 49, 50, 51, 51, 53, 54, 55, 55, 56, 56, 58, 59, 59, 60, 60, 61, 60, 62, 64, 63, 64, 65, 65, 67, 67, 68, 70, 69, 71
OFFSET
1,2
COMMENTS
The n-th convergent of the continued fraction expansion of Pi is A002485(n+1)/A002486(n+1).
LINKS
FORMULA
Limit_{n -> oo} a(n)/n = 2*log(A086702)/log(10) = 2*A100199/log(10) = 2*A240995. - A.H.M. Smeets, Jun 13 2018
EXAMPLE
From A.H.M. Smeets, Jun 13 2018: (Start)
Pi = 3.141592653589...
n=1: 3/1 = 3.0... so a(1) = 0;
n=2: 22/7 = 3.142... so a(2) = 2;
n=3: 333/106 = 3.14150... so a(3) = 4;
n=4: 355/113 = 3.1415929... so a(4) = 6;
n=5: 103993/33102 = 3.1415926530... so a(5) = 9;
n=6: 104348/33215 = 3.1415926539... so a(6) = 9;
n=7: 208341/66317 = 3.1415926534... so a(7) = 9;
n=8: 312689/99532 = 3.1415926536... so a(8) = 9;
n=9: 833719/265381 = 3.141592653581... so a(9) = 11;
n=10: 1146408/364913 = 3.14159265359... so a(10) = 10. (End)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Lekraj Beedassy, Jun 24 2003
EXTENSIONS
More terms from Vladeta Jovovic, Jun 27 2003
STATUS
approved