A288850 Number of distinct nonnegative rational numbers that can be obtained in n steps by a straight-line program (SLP) starting at 1 using addition, subtraction, multiplication and division.
1, 3, 6, 16, 58, 321, 2585, 30198
Offset: 0
Examples
The sets of numbers obtainable at the n-th step are:
S(0) = { 1 },
S(1) = { 0, 1, 2 },
S(2) = { 0, 1/2, 1, 2, 3, 4 },
S(3) = { 0, 1/4, 1/3, 1/2, 2/3, 1, 3/2, 2, 5/2, 3, 4, 5, 6, 8, 9, 16 }.
Links
- Hugo Pfoertner, Distribution of values generated by n-step SLPs, Illustration.
Extensions
a(7) from Alois P. Heinz, Jun 18 2017