This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225157 #6 May 01 2013 12:08:15 %S A225157 1,4,21,541,345181,136901485261,21135572172649245550621, %T A225157 496712610012943408146407697714437299262548141, %U A225157 271328559212953102170688304392824035451911661168940831351173011072850527195615099225368381 %N 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. %C A225157 Numerators of the sequence of fractions f(n) is A165423(n+1), hence sum(A165423(i+1)/a(i),i=1..n) = product(A165423(i+1)/a(i),i=1..n) = A165423(n+2)/A225164(n) = A176594(n-1)/A225164(n). %F A225157 a(n) = 5^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1. %F A225157 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. %e A225157 f(n) = 5, 5/4, 25/21, 625/541, ... %e A225157 5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ... %p A225157 b:=n->5^(2^(n-2)); # n > 1 %p A225157 b(1):=5; %p A225157 p:=proc(n) option remember; p(n-1)*a(n-1); end; %p A225157 p(1):=1; %p A225157 a:=proc(n) option remember; b(n)-p(n); end; %p A225157 a(1):=1; %p A225157 seq(a(i),i=1..9); %Y A225157 Cf. A100441, A165423, A176594, A225164. %K A225157 nonn,frac %O A225157 1,2 %A A225157 _Martin Renner_, Apr 30 2013