A185443 Engel expansion of A060997 = 1.433127...

1, 3, 4, 6, 6, 10, 10, 10, 21, 66, 207, 722, 6563, 25007, 372733, 2028763, 5472218, 41430101, 75142985, 192675195, 201216921, 925285050, 935598827, 2288358581, 2346034092, 26271379744, 41588896504, 152594692251, 529451874660

Offset: 1

Author

Jani Melik, Feb 04 2011

Keywords

• nonn

Links

• Eric W. Weisstein, Engel Expansion

Crossrefs

Cf. A006784.

Programs

Maple

Digits := 5000:
a0 := evalf(BesselI(0,2)/BesselI(1,2)):
f1 := proc(n) local i, an, u, a:
an := [ ]:
u := n:
for i from 1 to 30 do
   a := ceil(1/u):
   an := [ op(an), a ]:
   u := u * a - 1:
od:
RETURN (an): end:  f1(a0);

PARI

CFB(v)={ \\ converts a continued fraction to a number
my(x=v[#v]*1.);
forstep(i=#v-1,1,-1,
x = v[i] + x^-1;
);
x
};
Engel(x)={
my(v=List(),t);
while(1,
trap(,
return(Vec(v))
,
t = ceil(1/x)
);
listput(v,t);
x = (x * t) - 1
)
};
\p 500
Engel(CFB(vector(500,i,i)))

Extensions

gp script from Charles R Greathouse IV, Feb 06 2011