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.

1, 8, 73, 5977, 39556153, 1714946746986937, 3196895220321005409761642330233, 11033196234263169646028268239301916905952651329069957632398777

Offset: 1

Author

Martin Renner, Apr 30 2013

Keywords

• nonn

Comments

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).

Examples

			f(n) = 9, 9/8, 81/73, 6561/5977, ...
9 + 9/8 = 9 * 9/8 = 81/8; 9 + 9/8 + 81/73 = 9 * 9/8 * 81/73 = 6561/584; ...
		

Crossrefs

Cf. A011764, A100441, A165421, A165427, A225168.

Programs

Maple

b:=n->9^(2^(n-2)); # n > 1
b(1):=9;
p:=proc(n) option remember; p(n-1)*a(n-1); end;
p(1):=1;
a:=proc(n) option remember; b(n)-p(n); end;
a(1):=1;
seq(a(i),i=1..8);

Formula

a(n) = 9^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.

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.