cp's OEIS Frontend

A225162 Denominators of the sequence 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.

%I A225162 #5 May 01 2013 12:21:01
%S A225162 1,9,91,9181,92480761,9304615055139121,
%T A225162 93529710772930377727152664652641,
%U A225162 9394835719974970982728198049552322910011762062750179997188274881
%N A225162 Denominators of the sequence 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.
%C A225162 Numerators of the sequence of fractions f(n) is A165428(n+1), hence sum(A165428(i+1)/a(i),i=1..n) = product(A165428(i+1)/a(i),i=1..n) = A165428(n+2)/A225169(n) = A220812(n-1)/A225169(n).
%F A225162 a(n) = 10^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
%F A225162 a(n) = 10^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.
%e A225162 f(n) = 10, 10/9, 100/91, 10000/9181, ...
%e A225162 10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...
%p A225162 b:=n->10^(2^(n-2)); # n > 1
%p A225162 b(1):=10;
%p A225162 p:=proc(n) option remember; p(n-1)*a(n-1); end;
%p A225162 p(1):=1;
%p A225162 a:=proc(n) option remember; b(n)-p(n); end;
%p A225162 a(1):=1;
%p A225162 seq(a(i),i=1..8);
%Y A225162 Cf. A100441, A165428, A220812, A225169.
%K A225162 nonn
%O A225162 1,2
%A A225162 _Martin Renner_, Apr 30 2013