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

0,2

Links

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

Hugo Pfoertner, Distribution of values generated by n-step SLPs, Illustration.

Example

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 }.

Crossrefs

Cf. A216999, A288760, A288849.

Sequence in context: A201969 A367639 A340498 * A185629 A107885 A051271

Adjacent sequences: A288847 A288848 A288849 * A288851 A288852 A288853

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jun 18 2017

Extensions

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

Status

approved