

A084407


Number of decimal places to which the nth 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
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OFFSET

1,2


COMMENTS

The nth convergent of continued fraction expansion of Pi is A002485(n+1)/A002486(n+1).


LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..20000
F. Richman, Continued fractions


FORMULA

Lim {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.
Cf. A002485, A002486, A114526.
Cf. A086702, A100199, A240995.
Sequence in context: A176461 A255249 A330394 * A114526 A333387 A178126
Adjacent sequences: A084404 A084405 A084406 * A084408 A084409 A084410


KEYWORD

base,nonn


AUTHOR

Lekraj Beedassy, Jun 24 2003


EXTENSIONS

More terms from Vladeta Jovovic, Jun 27 2003


STATUS

approved



