First of all, my code doesn't do $N < 8 ... so you'd only expect to see correct answers from 5 on down.

Obvious. (Once someone kindly points it out.)

I'm getting the correct numbers for 14..17 when I run it so I'm guessing there's something else going on with either your testbed or mine

Indeed, mine! (A dumb typo.) 

C:\test>b-zeroBits.pl -N=1e5
Name "main::N" used only once: possible typo at C:\test\b-zeroBits.pl 
+line 1.
0100100010000100000100000010000000100000000100000000010000000000100000
+00000010000000
wrog: 1 : 0
wrog: 2 : 14
wrog: 3 : 5
wrog: 4 : 14
wrog: 5 : 14
wrog: 6 : 20
wrog: 7 : 27
wrog: 8 : 35
wrog: 9 : 44
wrog: 10 : 54
wrog: 11 : 65
wrog: 12 : 77
wrog: 13 : 90
wrog: 14 : 104
wrog: 15 : 119
wrog: 16 : 135
wrog: 17 : 152

[download]

My only excuse is attempting to give timely response to your efforts, whilst also construct a descent testbed and benchmark for 4 different approaches (3 posted + my own.). My own attempt -- essentially based on the ideas in the OP -- is proving to be a pain to code.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

In reply to Re^8: Locating a specified number of contiguous 0 bits within a large bitstring efficiently. by BrowserUk
in thread Locating a specified number of contiguous 0 bits within a large bitstring efficiently. by BrowserUk

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