cp's OEIS Frontend

A225160 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 8/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

%I A225160 #6 May 01 2013 12:20:10
%S A225160 1,7,57,3697,15302113,258902783918017,73384158961115901868286873473,
%T A225160 5848244449673109813614947741525727934929692392922517757697
%N A225160 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 8/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.
%C A225160 Numerators of the sequence of fractions f(n) is A165426(n+1), hence sum(A165426(i+1)/a(i),i=1..n) = product(A165426(i+1)/a(i),i=1..n) = A165426(n+2)/A225167(n) = A167182(n+2)/A225167(n).
%F A225160 a(n) = 8^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
%F A225160 a(n) = 8^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.
%e A225160 f(n) = 8, 8/7, 64/57, 4096/3697, ...
%e A225160 8 + 8/7 = 8 * 8/7 = 64/7; 8 + 8/7 + 64/57 = 8 * 8/7 * 64/57 = 4096/399; ...
%p A225160 b:=n->8^(2^(n-2)); # n > 1
%p A225160 b(1):=8;
%p A225160 p:=proc(n) option remember; p(n-1)*a(n-1); end;
%p A225160 p(1):=1;
%p A225160 a:=proc(n) option remember; b(n)-p(n); end;
%p A225160 a(1):=1;
%p A225160 seq(a(i),i=1..9);
%Y A225160 Cf. A100441, A165426, A167182, A225167.
%K A225160 nonn
%O A225160 1,2
%A A225160 _Martin Renner_, Apr 30 2013