cp's OEIS Frontend

A355615 Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(n + 1 - b(n-1)) for n > 1; a(n) is the numerator of b(n).

%I A355615 #17 Jul 11 2022 02:15:36
%S A355615 1,3,19,689,902919,1610893922869,5422187846648306990942459,
%T A355615 65408471597507349805723190837012905483968615226329
%N A355615 Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(n + 1 - b(n-1)) for n > 1; a(n) is the numerator of b(n).
%C A355615 The next term is too large to include.
%e A355615 The sequence {b(n)} begins 1, 3/2, 19/10, 689/310, 902919/363010, 1610893922869/594665194510, ...
%o A355615 (C++)
%o A355615 #include <boost/multiprecision/cpp_int.hpp>
%o A355615 #include <boost/rational.hpp>
%o A355615 #include <iostream>
%o A355615 using boost::multiprecision::cpp_int;
%o A355615 typedef boost::rational<cpp_int> rat;
%o A355615 int main() {
%o A355615   rat x(1);
%o A355615   int n = 1;
%o A355615   std::cout << "1\n";
%o A355615   while (++n < 10) {
%o A355615     x += rat(1)/(n+1-x);
%o A355615     std::cout << x.numerator() << '\n';
%o A355615   }
%o A355615 }
%Y A355615 Cf. A079278 (denominators).
%K A355615 nonn,frac
%O A355615 1,2
%A A355615 _Leonid Broukhis_, Jul 09 2022