MathDB

Starting with the sequence

F_1 = (1,2,3,4, \ldots)

of the natural numbers further sequences are generated as follows:

F_{n+1}

is created from

F_n

by the following rule: the order of elements remains unchanged, the elements from

F_n

which are divisible by

n

are increased by 1 and the other elements from

F_n

remain unchanged. Example:

F_2 = (2,3,4,5 \ldots)

and

F_3 = (3,3,5,5, \ldots)

. Determine all natural numbers

n

such that exactly the first

n-1

elements of

F_n

take the value

n.

Problem Statement