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(N=99)={localprec(N); my(c=2/Pi, d=c+c/10^N, 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]} \\ The optional argument is the precision used, approx. equal to the total number of digits in the result. - M. F. Hasler, Jul 04 2016
CROSSREFS
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