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A132201
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Pierce expansion of Catalan's Constant A006752.
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1
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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0.9159... = 1/1 - 1/11 + 1/(11*13) - 1/(11*13*59) + 1/(11*13*59*582) - ...
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(PARI) r=1/Catalan; for(n=1, 10, print(floor(r), ", "); r=r/(r-floor(r))) \\ G. C. Greubel, Nov 15 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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