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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}.
3
1, 3, 6, 24, 300, 37761, 451572162
OFFSET
0,2
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.
EXAMPLE
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 }.
CROSSREFS
KEYWORD
nonn,hard,more,nice
AUTHOR
Hugo Pfoertner, Jun 15 2017
EXTENSIONS
Wrong a(6) removed by Hugo Pfoertner, Jun 19 2017
a(6) from Markus Sigg, Jul 01 2017
STATUS
approved