On the Behavior of a Variant of Hofstadter ’ s Q-Sequence

  title={On the Behavior of a Variant of Hofstadter ’ s Q-Sequence},
  author={B. Balamohan and Alexander Kuznetsov and Stephen M. Tanny},
We completely solve the meta-Fibonacci recursion V (n) = V (n− V (n− 1)) + V (n− V (n− 4)), a variant of Hofstadter’s meta-Fibonacci Q-sequence. For the initial conditions V (1) = V (2) = V (3) = V (4) = 1 we prove that the sequence V (n) is monotone, with successive terms increasing by 0 or 1, so the sequence hits every positive integer. We demonstrate certain special structural properties and fascinating periodicities of the associated frequency sequence (the number of times V (n) hits each… CONTINUE READING
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