login
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).
1
1, 3, 19, 689, 902919, 1610893922869, 5422187846648306990942459, 65408471597507349805723190837012905483968615226329
OFFSET
1,2
COMMENTS
The next term is too large to include.
EXAMPLE
The sequence {b(n)} begins 1, 3/2, 19/10, 689/310, 902919/363010, 1610893922869/594665194510, ...
PROG
(C++)
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/rational.hpp>
#include <iostream>
using boost::multiprecision::cpp_int;
typedef boost::rational<cpp_int> rat;
int main() {
rat x(1);
int n = 1;
std::cout << "1\n";
while (++n < 10) {
x += rat(1)/(n+1-x);
std::cout << x.numerator() << '\n';
}
}
CROSSREFS
Cf. A079278 (denominators).
Sequence in context: A337528 A136372 A272571 * A329470 A107706 A373626
KEYWORD
nonn,frac
AUTHOR
Leonid Broukhis, Jul 09 2022
STATUS
approved