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.

1, 9, 91, 9181, 92480761, 9304615055139121, 93529710772930377727152664652641, 9394835719974970982728198049552322910011762062750179997188274881

Offset: 1

Author

Martin Renner, Apr 30 2013

Keywords

• nonn

Comments

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).

Examples

			f(n) = 10, 10/9, 100/91, 10000/9181, ...
10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...
		

Crossrefs

Cf. A100441, A165428, A220812, A225169.

Programs

Maple

b:=n->10^(2^(n-2)); # n > 1
b(1):=10;
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) = 10^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.

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.