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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 (list; graph; refs; listen; history; text; internal format)
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
Cf. A000796.
Sequence in context: A176461 A255249 A330394 * A114526 A333387 A178126
KEYWORD
base,nonn
AUTHOR
Lekraj Beedassy, Jun 24 2003
EXTENSIONS
More terms from Vladeta Jovovic, Jun 27 2003
STATUS
approved

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Last modified June 24 09:58 EDT 2024. Contains 373674 sequences. (Running on oeis4.)