cp's OEIS Frontend

A225161 Denominators of the sequence 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.

%I A225161 #5 May 01 2013 12:20:41
%S A225161 1,8,73,5977,39556153,1714946746986937,
%T A225161 3196895220321005409761642330233,
%U A225161 11033196234263169646028268239301916905952651329069957632398777
%N A225161 Denominators of the sequence 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.
%C A225161 Numerators of the sequence of fractions f(n) is A165427(n+1), hence sum(A165427(i+1)/a(i),i=1..n) = product(A165427(i+1)/a(i),i=1..n) = A165427(n+2)/A225168(n) = A165421(n+3)/A225168(n) = A011764(n)/A225168(n).
%F A225161 a(n) = 9^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
%F A225161 a(n) = 9^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.
%e A225161 f(n) = 9, 9/8, 81/73, 6561/5977, ...
%e A225161 9 + 9/8 = 9 * 9/8 = 81/8; 9 + 9/8 + 81/73 = 9 * 9/8 * 81/73 = 6561/584; ...
%p A225161 b:=n->9^(2^(n-2)); # n > 1
%p A225161 b(1):=9;
%p A225161 p:=proc(n) option remember; p(n-1)*a(n-1); end;
%p A225161 p(1):=1;
%p A225161 a:=proc(n) option remember; b(n)-p(n); end;
%p A225161 a(1):=1;
%p A225161 seq(a(i),i=1..8);
%Y A225161 Cf. A011764, A100441, A165421, A165427, A225168.
%K A225161 nonn
%O A225161 1,2
%A A225161 _Martin Renner_, Apr 30 2013