A225168 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 9/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

1, 8, 584, 3490568, 138073441864904, 236788599971507074896206759048, 756988343475413525492604622110601759725560263205883476698184

Offset

1,2

Comments

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165427(n+2), hence sum(A165427(i+1)/A225161(i),i=1..n) = product(A165427(i+1)/A225161(i),i=1..n) = A165427(n+2)/a(n) = A165421(n+3)/a(n) = A011764(n)/a(n).

Links

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

Formula

a(n) = 9^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/9.

Example

f(n) = 9, 9/8, 81/73, 6561/5977, ...
9 + 9/8 = 9 * 9/8 = 81/8; 9 + 9/8 + 81/73 = 9 * 9/8 * 81/73 = 6561/584; ...
s(n) = 1/b(n) = 9, 81/8, 6561/584, ...

Maple

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/9;
a:=n->9^(2^(n-1))*b(n);
seq(a(i), i=1..8);

Crossrefs

Cf. A011764, A076628, A165421, A165427, A225161.

Sequence in context: A303933 A188780 A015023 * A332158 A269508 A090923

Adjacent sequences: A225165 A225166 A225167 * A225169 A225170 A225171

Keyword

nonn

Author

Martin Renner, Apr 30 2013

Status

approved