A014012 Engel expansion of 1/Pi.

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

Offset: 1

Author

Simon Plouffe

Keywords

• nonn

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

Crossrefs

See A006784 for definition.

Programs

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 *)