Pi Hunting - find an index of Pi whose value matches its index
Python 2, 64 bytes

i=1
while i&lt;len(P):
&#9;if int(P[i:i+len(str(i))])==i:print i
&#9;i+=1

As you said, pi's digits are given, so I chose the variable P to contain the entire digit string.
The full code first downloads one billion digits of pi to a file using cURL and then reads in that file to process it.

&quot;Setting up pi's digits.&quot;; exec'import os\nN,f=200000000,&quot;pi.txt&quot;\nif not os.path.exists(f):os.system(&quot;curl https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt&gt;&quot;+f)\nP=open(f,&quot;r&quot;).read()[1:N+2][:-1]'
&quot;Search through pi.&quot;;      exec'i=1\nwhile i&lt;len(P):\n\tif int(P[i:i+len(str(i))])==i:print i\n\ti+=1'

Though, when one knows the answer, a simple plaintext output is actually shorter (29 bytes).

print&quot;1,16470,44899,79873884&quot;

This series of numbers is also known to the OEIS (http://oeis.org/A057680).