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A014012 Engel expansion of 1/Pi. 3
4, 4, 11, 45, 70, 1111, 4423, 5478, 49340, 94388, 200677, 308749, 708066, 711391, 1113024, 4342375, 4529119, 8061070, 12060867, 56215509, 69737317, 124001030, 214920537, 471564389, 891380746, 4293367334, 5031151602, 9832878719, 15034446439, 15481444638 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Simon Plouffe, Table of n, a(n) for n = 1..973 [Terms 1 through 300 were computed by T. D. Noe]

Index entries for sequences related to Engel expansions

MAPLE

a(n):=proc(s)

local

i, j, max, aa, bb, lll, prod, S, T, kk;

    S := evalf(abs(s));

    max := 10^(Digits - 10);

    prod := 1;

    lll := [];

    while prod <= max do

        T := 1 + trunc(1/S);

        S := frac(S*T);

        lll := [op(lll), T];

        prod := prod*T

    end do;

    RETURN(lll)

end;

### Enter a real number and the program will return the Engel expansion of that number, the number of terms is adjusted to the output

# Simon Plouffe, Apr 23 2016

MATHEMATICA

EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[1/Pi, 7! ], 50] (* Vladimir Joseph Stephan Orlovsky, Jun 08 2009 *)

CROSSREFS

See A006784 for definition.

Sequence in context: A048223 A214112 A211950 * A273391 A273452 A178182

Adjacent sequences:  A014009 A014010 A014011 * A014013 A014014 A014015

KEYWORD

nonn

AUTHOR

Simon Plouffe

STATUS

approved

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Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)