integer sequence defined recursively HELP!

[BIGHOSS]

I am struggling in my class and I could use some help with this...Can someone help enplane this to me in layman's terms I am a visual learner and have a hard time understanding how the book enplanes things...

Let a1, a2, a3, . . . be the integer sequence defined recursively by
1) a1 = 0;
and 2) For n > 1, an =1 + a[n/2].

Find an explicit formula for an and prove that your formula is correct.

 

[daon2]

\(\displaystyle a_1=0\)

\(\displaystyle a_2=1+a_{\left[ 2/2\right]}= 1+a_1 = 1\)

\(\displaystyle a_3=1+a_{\left[ 3/2\right]} = 1+a_1 = 1\)

\(\displaystyle a_4=1+a_{\left[ 4/2\right]} = 1+a_2 = 2\)

\(\displaystyle a_5=1+a_{\left[ 5/2\right]} = 1+a_2 = 2\)

seeing something?