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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
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
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.)