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

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