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 A132201 Pierce expansion of Catalan's Constant A006752. 1
 1, 11, 13, 59, 582, 12285, 127893, 654577, 1896651, 2083263, 3828867, 6195679, 22339606, 43877386, 209882043, 269091773, 1585394894, 2614512078, 3726537414, 4487682121, 6296491774, 8648456991, 23933983277, 174313954158, 367633382556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 T. A. Pierce, On an algorithm and its use in approximating roots of algebraic equations, Am. Math. Monthly 36 (10) (1929) 523. Eric Weisstein's World of Mathematics, Pierce Expansion. EXAMPLE 0.9159... = 1/1 - 1/11 + 1/(11*13) - 1/(11*13*59) + 1/(11*13*59*582) - ... MAPLE Digits := 300: Pierce := proc(x) local resid, a, i, an ; resid := x ; a := [] ; for i from 1 do an := floor(1./resid) ; a := [op(a), an] ; resid := evalf(1.-an*resid) ; if ilog10( mul(i, i=a)) > 0.7*Digits then break ; fi ; od: RETURN(a) ; end: Pierce(Catalan); 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[Catalan , 7!], 20] (* G. C. Greubel, Nov 15 2016 *) PROG (PARI) r=1/Catalan; for(n=1, 10, print(floor(r), ", "); r=r/(r-floor(r))) \\ G. C. Greubel, Nov 15 2016 CROSSREFS Cf. A006752. Sequence in context: A027450 A234799 A036295 * A057189 A072580 A186640 Adjacent sequences: A132198 A132199 A132200 * A132202 A132203 A132204 KEYWORD nonn AUTHOR R. J. Mathar, Nov 05 2007 STATUS approved

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Last modified February 20 19:36 EST 2024. Contains 370217 sequences. (Running on oeis4.)