Dyalog APL, 11

(-∘1+⍳⌈/)+/

Try it here. Usage:

   f ← (-∘1+⍳⌈/)+/
   4 f 0 1 1 0 1 1 1 0 0 0 0 1 1
1

Explanation

This is a dyadic (meaning binary) function that takes the substring length from the left, and the sequence from the right. Its structure is the following:

   ┌───┴────┐
 ┌─┴──┐     /
 ∘  ┌─┼─┐ ┌─┘
┌┴┐ + ⍳ / +  
- 1   ┌─┘    
      ⌈      

So, the topmost branch is a hook of two functions, +/ and -∘1+⍳⌈/, which means that given inputs n and x, we evaluate n +/ x (the sums of length-n substrings of x) and feed that to -∘1+⍳⌈/. This function, on the other hand, is a hook of -∘1 (subtract 1) and the fork +⍳⌈/. This means that the result of n +/ x above (let's call it y) is given to both + (which is the identity when only one argument is given) and ⌈/ (which finds the maximum of y), and the results are given to ⍳, which returns the first index of the right argument in the left. We have to subtract 1 from this, since APL lists are 1-indexed.

As an example, let's take 4 and 0 1 1 0 1 1 1 0 as inputs. First we apply +/ to them and get 2 3 3 3 3. Then, + and ⌈/ applied to this list give the list itself and 3, and 2 3 3 3 3 ⍳ 3 evaluates to 2, since 3 first occurs as the second element. We subtract 1 and get 1 as the final result.

Dyalog APL, 11

(-∘1+⍳⌈/)+/

Try it here. Usage:

   f ← (-∘1+⍳⌈/)+/
   4 f 0 1 1 0 1 1 1 0 0 0 0 1 1
1

Explanation

This is a dyadic (meaning binary) function that takes the substring length from the left, and the sequence from the right. Its structure is the following:

   ┌───┴────┐
 ┌─┴──┐     /
 ∘  ┌─┼─┐ ┌─┘
┌┴┐ + ⍳ / +  
- 1   ┌─┘    
      ⌈      

Explanation by explosion:

(-∘1+⍳⌈/)+/
(       )+/  ⍝ Take sums of substrings of given length, and feed to function in parentheses
    + ⌈/     ⍝ The array of sums itself, and its maximum
     ⍳       ⍝ First index of right argument in left
 -∘1         ⍝ Subtract 1 (APL arrays are 1-indexed)

As an example, let's take 4 and 0 1 1 0 1 1 1 0 as inputs. First we apply the function +/ to them and get 2 3 3 3 3. Then, + and ⌈/ applied to this array give itself and 3, and 2 3 3 3 3 ⍳ 3 evaluates to 2, since 3 first occurs as the second element. We subtract 1 and get 1 as the final result.

Dyalog APL, 11

(-∘1+⍳⌈/)+/

Try it here. Usage:

   f ← (-∘1+⍳⌈/)+/
   4 f 0 1 1 0 1 1 1 0 0 0 0 1 1
1

Explanation coming soon.

Dyalog APL, 11

(-∘1+⍳⌈/)+/

Try it here. Usage:

   f ← (-∘1+⍳⌈/)+/
   4 f 0 1 1 0 1 1 1 0 0 0 0 1 1
1

Explanation

This is a dyadic (meaning binary) function that takes the substring length from the left, and the sequence from the right. Its structure is the following:

   ┌───┴────┐
 ┌─┴──┐     /
 ∘  ┌─┼─┐ ┌─┘
┌┴┐ + ⍳ / +  
- 1   ┌─┘    
      ⌈      

So, the topmost branch is a hook of two functions, +/ and -∘1+⍳⌈/, which means that given inputs n and x, we evaluate n +/ x (the sums of length-n substrings of x) and feed that to -∘1+⍳⌈/. This function, on the other hand, is a hook of -∘1 (subtract 1) and the fork +⍳⌈/. This means that the result of n +/ x above (let's call it y) is given to both + (which is the identity when only one argument is given) and ⌈/ (which finds the maximum of y), and the results are given to ⍳, which returns the first index of the right argument in the left. We have to subtract 1 from this, since APL lists are 1-indexed.

As an example, let's take 4 and 0 1 1 0 1 1 1 0 as inputs. First we apply +/ to them and get 2 3 3 3 3. Then, + and ⌈/ applied to this list give the list itself and 3, and 2 3 3 3 3 ⍳ 3 evaluates to 2, since 3 first occurs as the second element. We subtract 1 and get 1 as the final result.