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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, MathWorld.

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 October 14 04:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)