The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 81 – 100 of 250

Showing per page

On a functional-differential equation related to Golomb's self-described sequence

Y.-F. S. Pétermann, J.-L. Rémy, I. Vardi (1999)

Journal de théorie des nombres de Bordeaux

The functional-differential equation f ' ( t ) = 1 / f ( f ( t ) ) is closely related to Golomb’s self-described sequence F , 1 , 1 , 2 , 2 , 2 , 3 , 3 , 2 , 4 , 4 , 4 3 , 5 , 5 , 5 , 3 , 6 , 6 , 6 , 6 , 4 , . We describe the increasing solutions of this equation. We show that such a solution must have a nonnegative fixed point, and that for every number p 0 there is exactly one increasing solution with p as a fixed point. We also show that in general an initial condition doesn’t determine a unique solution: indeed the graphs of two distinct increasing solutions cross each other infinitely many times. In fact...

Currently displaying 81 – 100 of 250