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 A006283 Pierce expansion for 1 / Pi. (Formerly M3092) 10
 3, 22, 118, 383, 571, 635, 70529, 375687, 399380, 575584, 699357, 1561065, 1795712, 194445473, 253745996, 3199003690, 3727084011, 6607433185, 16248462801, 172940584814, 313728984965, 796022309187, 5348508258636, 5962546521072, 97497255361780, 121347007731845 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sequence can be produced with the unit circle: a(1) = number of diameter length arcs in circle rounded down to nearest integer (remainder arc = x_1). a(2) = number of x_1 length arcs in circle rounded down to nearest integer (remainder arc = x_2). a(3) = number of x_2 length arcs in circle rounded down to nearest integer (remainder arc = x_3). And so on ... . - Peter Woodward, Sep 08 2016 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 Jeffrey Shallit, Some predictable Pierce expansions, Fib. Quart., 22 (1984), 332-335. Eric Weisstein's World of Mathematics, Pierce Expansion EXAMPLE Let x_0 = 1/Pi = 0.318309886... and a(0) = floor(1/x_0) = 3. Then set x_1 = 1 - a_0*x_0 = 0.0450703..., and a(1) = floor(1/x_1) = 22. Then x_2 = 1 - a_1*x_1 = 0.008452..., and a(2) = floor(1/x2) = 118. - Michael B. Porter, Sep 09 2016 MATHEMATICA PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[1/Pi, 8!], 50] (* G. C. Greubel, Nov 13 2016 *) PROG (PARI) default(realprecision, 100000); r=Pi; for(n=1, 100, s=(r/(r-floor(r))); print1(floor(r), ", "); r=s) \\ Benoit Cloitre [amended by Georg Fischer, Nov 20 2020] CROSSREFS Cf. A154956 (analog for 2/Pi). Sequence in context: A309000 A061182 A143552 * A232017 A100511 A033506 Adjacent sequences:  A006280 A006281 A006282 * A006284 A006285 A006286 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)