A225159 - OEIS

%I #6 May 01 2013 12:19:34

%S 1,6,43,2143,5211907,30351298460743,1016966398053911225889737707,

%T 1130815308619683511655208290917557601522304473342184143

%N Denominators of the sequence of fractions f(n) defined recursively by f(1) = 7/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

%C Numerators of the sequence of fractions f(n) is A165425(n+1), hence sum(A165425(i+1)/a(i),i=1..n) = product(A165425(i+1)/a(i),i=1..n) = A165425(n+2)/A225166(n).

%F a(n) = 7^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.

%F a(n) = 7^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.

%e f(n) = 7, 7/6, 49/43, 2401/2143, ...

%e 7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ...

%p b:=n->7^(2^(n-2)); # n > 1

%p b(1):=7;

%p p:=proc(n) option remember; p(n-1)*a(n-1); end;

%p p(1):=1;

%p a:=proc(n) option remember; b(n)-p(n); end;

%p a(1):=1;

%p seq(a(i),i=1..9);

%Y Cf. A100441, A165425, A225166.

%K nonn

%O 1,2

%A _Martin Renner_, Apr 30 2013