A288760 Number of distinct nonnegative 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}.

1, 3, 6, 24, 300, 37761, 451572162

Offset: 0

Author

Hugo Pfoertner, Jun 15 2017

Keywords

• nonn
• hard
• more
• nice

Comments

The conjectured value of a(6)=451572162 needs independent verification.

For an explanation of the difference from a straight-line program (SLP) see comment in A288759. A288850 provides the corresponding cardinalities of the sets that can be obtained by an n-step SLP.

Examples

			The sets of numbers >=0 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, 1/8, 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 }.
		

Links

• Hugo Pfoertner, Illustration of the Distribution of values generated in steps 3, 4, 5, 6
• Index to sequences related to the complexity of n

Crossrefs

Cf. A214872, A216999, A288759, A288850.

Extensions

Wrong a(6) removed by Hugo Pfoertner, Jun 19 2017

a(6) from Markus Sigg, Jul 01 2017