9 billion names of God the integer
This task is a variation of the short story by Arthur C. Clarke.
(Solvers should be aware of the consequences of completing this task.)
In detail, to specify what is meant by a "name":
- The integer 1 has 1 name "1".
- The integer 2 has 2 names "1+1" and "2".
- The integer 3 has 3 names "1+1+1", "2+1", and "3".
- The integer 4 has 5 names "1+1+1+1", "2+1+1", "2+2", "3+1", "4".
- The integer 5 has 7 names "1+1+1+1+1", "2+1+1+1", "2+2+1", "3+1+1", "3+2", "4+1", "5".
This can be visualized in the following form:
1
1 1
1 1 1
1 2 1 1
1 2 2 1 1 1 3 3 2 1 1
Where row $n$ corresponds to integer $n$, and each column $C$ in row $m$ from left to right corresponds to the number of names beginning with $C$.
Optionally note that the sum of the $n$-th row $P(n)$ is the integer partition function.
Test
{{test}}Console output