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, 3, 19, 689, 902919, 1610893922869, 5422187846648306990942459, 65408471597507349805723190837012905483968615226329

Offset

1,2

Comments

The next term is too large to include.

Links

Table of n, a(n) for n=1..8.

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

Adjacent sequences: A355612 A355613 A355614 * A355616 A355617 A355618

Keyword

nonn,frac

Author

Leonid Broukhis, Jul 09 2022

Status

approved