Sequencing

Probability Level 2

The Hofstadter Q sequence is defined as follows:

  • Q ( 1 ) = Q ( 2 ) = 1 Q(1) = Q(2) = 1 ,

  • For n > 2 n > 2 , Q ( n ) Q(n) satisfy the relationship: Q ( n ) = Q ( n − Q ( n − 1 ) ) + Q ( n − Q ( n − 2 ) ) Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2))

What is the first n n such that Q ( n ) > [ Q ( n − 1 ) + 1 ] Q(n) > [Q(n-1) + 1] ?


The answer is 12.

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Mar 5, 2016

Q(1) = Q(2) = 1
Q(3) = 2
Q(4) = Q(5) = 3
Q(6) =4
Q(7) = Q(8) = 5
Q(9) = Q(10) = Q(11) = 6
Q(12) = 8 (first jump of more than 1)


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Moderator note:

What is special about this Sequence?

E.g. Is the function non-decreasing?

It is not. Q(15) = 10, Q(16) = 9.

Denton Young - 5 years, 3 months ago

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