A225163 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 3/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

1, 2, 14, 938, 5274374, 199225484935778, 329478051871899046990657602014, 1022767669188735114815831063606918316150663428260080434555738

Offset

1,2

Comments

Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165421(n+2), hence s(n) = sum(A165421(i+1)/A225156(i),i=1..n) = product(A165421(i+1)/A225156(i),i=1..n) = A165421(n+2)/a(n) = A011764(n-1)/a(n).

Links

Table of n, a(n) for n=1..8.

Paul Yiu, Recreational Mathematics, Department of Mathematics, Florida Atlantic University, 2003, Chapter 5.4, p. 207 (Project).

Formula

a(n) = 3^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/3.

Example

f(n) = 3, 3/2, 9/7, 81/67, ...
3 + 3/2 = 3 * 3/2 = 9/2; 3 + 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14; ...
s(n) = 1/b(n) = 3, 9/2, 81/14, ...

Maple

b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
b(1):=1/3;
a:=n->3^(2^(n-1))*b(n);
seq(a(i), i=1..9);

Crossrefs

Cf. A011764, A076628, A165421, A225156.

Sequence in context: A065868 A032419 A144017 * A319540 A190634 A130421

Adjacent sequences: A225160 A225161 A225162 * A225164 A225165 A225166

Keyword

nonn

Author

Martin Renner, Apr 30 2013

Status

approved