A225169 - OEIS

A225169

Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 10/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

1, 9, 819, 7519239, 695384944860879, 6470289227069622272847335347359, 605164280025029017271801950447677089988237937249820002811725119

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165428(n+2), hence sum(A165428(i+1)/A225162(i),i=1..n) = product(A165428(i+1)/A225162(i),i=1..n) = A165428(n+2)/a(n) = A220812(n-1)/a(n).

LINKS

Table of n, a(n) for n=1..7.

FORMULA

a(n) = 10^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/10.

EXAMPLE

f(n) = 10, 10/9, 100/91, 10000/9181, ...

10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...

s(n) = 1/b(n) = 10, 100/9, 10000/819, ...

MAPLE

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:

b(1):=1/10;

a:=n->10^(2^(n-1))*b(n);