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A154956 Pierce expansion of 2/Pi. 3
1, 2, 3, 5, 10, 71, 868, 1788, 7455, 44266, 54626, 74153, 224166, 390471, 1489304, 3737961, 22277163, 37201631, 113275744, 165029426, 2642368758, 3362202939, 5191046363, 8438525012, 36226438506, 40174126779, 125336047846, 531802867080, 599020778171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Simon Plouffe and G. C. Greubel, Table of n, a(n) for n = 0..500 (terms from 0 to 216 were computed by Simon Plouffe)

EXAMPLE

1 - 1/2(1 - 1/3(1 - 1/5(1 - 1/10(1 - 1/71)))) = 2/(355/113).

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: a060294 := evalf(2/Pi) ; Pierce(a060294) ; # R. J. Mathar, Jan 21 2009

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[2/Pi, 7!], 50] (* G. C. Greubel, Nov 13 2016 *)

PROG

(PARI) A154956(c=2/Pi, d=c+c/10^(default(realprecision)-1), a=[1\c])={while(a[#a]==1\d&&c=1-c*a[#a], d=1-d*a[#a]; a=concat(a, 1\c)); a[^-1]} \\ M. F. Hasler, Jul 04 2016

CROSSREFS

Cf. A006283 (1/Pi), A061233 (4 - Pi).

Cf. A060294 (decimal expansion of 2/Pi). - R. J. Mathar, Jan 21 2009

Sequence in context: A213169 A003182 A134294 * A197312 A259387 A130165

Adjacent sequences:  A154953 A154954 A154955 * A154957 A154958 A154959

KEYWORD

nonn

AUTHOR

Jaume Oliver Lafont, Jan 18 2009

EXTENSIONS

More terms from R. J. Mathar, Jan 21 2009

Offset in b-file corrected by N. J. A. Sloane, Aug 31 2009

STATUS

approved

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Last modified July 16 12:19 EDT 2019. Contains 325079 sequences. (Running on oeis4.)