A288760 -id:A288760 - cp's OEIS frontend

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

Hugo Pfoertner, Jun 18 2017

			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 }.

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

Cf. A216999, A288760, A288849.

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

A288759 Number of distinct rational numbers that can be obtained in n steps by applying addition, subtraction, multiplication and division to any two potentially identical numbers from the complete set of numbers created in n-1 steps, starting with the set {1}.

Original entry on oeis.org

1, 3, 8, 38, 555, 74423, 902663448

Offset: 0

Hugo Pfoertner, Jun 15 2017

This is different from a straight-line program (SLP), which can only use numbers created in the path to its own result at level n-1. A288849 provides the cardinalities of the sets that can be created by the related SLPs.

			The sets of numbers obtainable at the n-th step are:
S(0) = { 1 },
S(1) = { 0, 1, 2 },
S(2) = { -2, -1, 0, 1/2, 1, 2, 3, 4 },
S(3) = { -8, -6, -5, -4, -7/2, -3, -5/2, -2, -3/2, -1, -2/3, -1/2, -1/3, -1/4, 0, 1/8, 1/6, 1/4, 1/3, 1/2, 2/3, 3/4, 1, 4/3, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 6, 7, 8, 9, 12, 16 }.

Cf. A214872, A216999, A288760, A288849.

a(6) from Hugo Pfoertner and Markus Sigg, Aug 06 2017

cp's OEIS Frontend

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.

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