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Vladimir Reshetnikov
Vladimir Reshetnikov
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For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive algebraic numbers? Is it exactly the seta superset of positive algebraic numbers? Is it countable? Is $2^{\sqrt 2}$ or $\log_2 3$ in the set?

For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive algebraic numbers?

For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive algebraic numbers? Is it a superset of positive algebraic numbers? Is it countable? Is $2^{\sqrt 2}$ or $\log_2 3$ in the set?

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Vladimir Reshetnikov
Vladimir Reshetnikov
  • 6.8k
  • 2
  • 53
  • 87

Number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways

For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive algebraic numbers?