A225157 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 5/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.
1, 4, 21, 541, 345181, 136901485261, 21135572172649245550621, 496712610012943408146407697714437299262548141, 271328559212953102170688304392824035451911661168940831351173011072850527195615099225368381
Offset: 1
Examples
f(n) = 5, 5/4, 25/21, 625/541, ... 5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ...
Programs
-
Maple
b:=n->5^(2^(n-2)); # n > 1 b(1):=5; 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..9);
Formula
a(n) = 5^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
a(n) = 5^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.
Comments