A288849 Number of distinct 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, 7, 21, 83, 484, 4084, 49479

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Example

The sets of numbers obtainable at the n-th step are:
S(0) = { 1 },
S(1) = { 0, 1, 2 },
S(2) = { -1, 0, 1/2, 1, 2, 3, 4 },
S(3) = { -3, -2, -3/2, -1, -1/2, 0, 1/4, 1/3, 1/2, 2/3, 1, 3/2, 2, 5/2, 3, 4, 5, 6, 8, 9, 16 }.

Crossrefs

Cf. A214872, A288759, A288850.

A216999 provides the corresponding results if division is not used.

Sequence in context: A319123 A173794 A049365 * A031885 A259202 A169981

Adjacent sequences: A288846 A288847 A288848 * A288850 A288851 A288852

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jun 18 2017

Extensions

a(7) from Alois P. Heinz, Jun 18 2017

Status

approved