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%I #33 Jul 01 2017 08:43:04
%S 1,3,6,24,300,37761,451572162
%N 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}.
%C The conjectured value of a(6)=451572162 needs independent verification.
%C 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.
%H Hugo Pfoertner, <a href="/A288760/a288760.pdf">Illustration of the Distribution of values generated in steps 3, 4, 5, 6</a>
%H <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%e The sets of numbers >=0 obtainable at the n-th step are:
%e S(0) = { 1 },
%e S(1) = { 0, 1, 2 },
%e S(2) = { 0, 1/2, 1, 2, 3, 4 },
%e 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 }.
%Y Cf. A214872, A216999, A288759, A288850.
%K nonn,hard,more,nice
%O 0,2
%A _Hugo Pfoertner_, Jun 15 2017
%E Wrong a(6) removed by _Hugo Pfoertner_, Jun 19 2017
%E a(6) from _Markus Sigg_, Jul 01 2017