A185443 - OEIS

%I #14 May 13 2013 01:49:31

%S 1,3,4,6,6,10,10,10,21,66,207,722,6563,25007,372733,2028763,5472218,

%T 41430101,75142985,192675195,201216921,925285050,935598827,2288358581,

%U 2346034092,26271379744,41588896504,152594692251,529451874660

%N Engel expansion of A060997 = 1.433127...

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>

%p Digits := 5000:

%p a0 := evalf(BesselI(0,2)/BesselI(1,2)):

%p f1 := proc(n) local i, an, u, a:

%p an := [ ]:

%p u := n:

%p for i from 1 to 30 do

%p    a := ceil(1/u):

%p    an := [ op(an), a ]:

%p    u := u * a - 1:

%p od:

%p RETURN (an): end:  f1(a0);

%o (PARI) CFB(v)={ \\ converts a continued fraction to a number

%o my(x=v[#v]*1.);

%o forstep(i=#v-1,1,-1,

%o x = v[i] + x^-1;

%o );

%o x

%o };

%o Engel(x)={

%o my(v=List(),t);

%o while(1,

%o trap(,

%o return(Vec(v))

%o ,

%o t = ceil(1/x)

%o );

%o listput(v,t);

%o x = (x * t) - 1

%o )

%o };

%o \p 500

%o Engel(CFB(vector(500,i,i)))

%Y Cf. A006784.

%K nonn

%O 1,2

%A _Jani Melik_, Feb 04 2011

%E gp script from _Charles R Greathouse IV_, Feb 06 2011