RosettaCodeData/Task/Hofstadter-Q-sequence/00DESCRIPTION

The [[wp:Hofstadter_sequence#Hofstadter_Q_sequence|Hofstadter Q sequence]] is defined as:
<big>
:: <math>\begin{align}
Q(1)&=Q(2)=1, \\
Q(n)&=Q\big(n-Q(n-1)\big)+Q\big(n-Q(n-2)\big), \quad n>2.
\end{align}</math>
</big>

It is defined like the [[Fibonacci sequence]], but whereas the next term in the Fibonacci sequence is the sum of the previous two terms, in the Q sequence the previous two terms tell you how far to go back in the Q sequence to find the two numbers to sum to make the next term of the sequence.


;Task:
* Confirm and display that the first ten terms of the sequence are: 1, 1, 2, 3, 3, 4, 5, 5, 6, and 6
* Confirm and display that the 1000<sup>th</sup> term is: &nbsp; 502


;Optional extra credit
* Count and display how many times a member of the sequence is less than its preceding term for terms up to and including the 100,000<sup>th</sup> term.
* Ensure that the extra credit solution &nbsp; ''safely'' &nbsp; handles being initially asked for an '''n'''<sup>th</sup> term where &nbsp; '''n''' &nbsp; is large.
<br>(This point is to ensure that caching and/or recursion limits, if it is a concern, is correctly handled).
<br><br>