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
Keywords
Examples
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, ...
Programs
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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);
Formula
a(n) = 9^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/9.
Comments