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 July 7th, 2012, 12:09 PM #1 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Functional equation with a recurrence relation. I rarely post on this section but this time I've got a real problem. Consider the recurrence function: $L(n)= L(\left \lfloor \frac{n}{2} \right \rfloor) + 1 \text{ and } L(1) = 0$ My goal is to find the functional form of L(n). From examining the first 17 outputs, I conclude that this function is related to logarithmic function. Thank you all.
 July 7th, 2012, 02:53 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,027 Thanks: 2258 You need to revise the definition so that it doesn't imply L(0) = L(0) + 1, which is impossible.
July 7th, 2012, 11:43 PM   #3
Math Team

Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory

Quote:
 Originally Posted by skipjack You need to revise the definition so that it doesn't imply L(0) = L(0) + 1, which is impossible.
L(0) is undefiend.

With the use of advanced GDC, theory of curve fitting and purely iterative algorithms, I found:
$L(n)= \left \lfloor lg(n) \right \rfloor$

But cannot prove it without iteration.

Any help is appritiated.

 Tags equation, functional, recurrence, relation

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