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A063674 Numerators of increasingly better rational approximations to Pi with increasing denominators (3/1, 13/4, 16/5, 19/6, 22/7, 179/57, ...) 7
3, 13, 16, 19, 22, 179, 201, 223, 245, 267, 289, 311, 333, 355, 52163, 52518, 52873, 53228, 53583, 53938, 54293, 54648, 55003, 55358, 55713, 56068, 56423, 56778, 57133, 57488, 57843, 58198, 58553, 58908, 59263, 59618, 59973, 60328, 60683, 61038, 61393, 61748 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numerators of the sequence (3/1, 13/4, 16/5, 19/6, 22/7, 179/57, 201/64, 223/71, 245/78, 267/85, 289/92, 311/99, 333/106, 355/113, 52163/16604, 52518/16717, ...)
Large jumps occur after the classical approximations 22/7 and 355/113, which are sufficiently precise to require a much larger denominator for a better approximation. - M. F. Hasler, Apr 01 2013
LINKS
Jean-Louis Sikorav, Best rational approximations of an irrational number, arXiv:1807.06284 [math.NT], 2018.
MATHEMATICA
piapprox[n_] := Block[{a, i}, a = {3/1}; For[i = 2, i <= n, i++, If[Abs[Round[i Pi]/i - Pi] < Abs[Last[a] - Pi], AppendTo[a, Round[i Pi]/i], Null]]; Return[a]] (* Suren Fernando via Alexander R. Povolotsky, Aug 03 2008 *)
PROG
(PARI) {e=1; for(d=1, 1e5, abs( Pi-round(Pi*d)/d ) < e & !print1(round(Pi*d)", ") & e=abs(Pi - round(Pi*d)/d))} \\ [M. F. Hasler, Apr 01 2013]
CROSSREFS
Sequence in context: A216044 A023144 A152269 * A273678 A022124 A042133
KEYWORD
frac,nonn
AUTHOR
Suren L. Fernando (fernando(AT)truman.edu), Jul 27 2001
EXTENSIONS
More terms from M. F. Hasler, Apr 01 2013
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)