xor(1..n) = switch(n % 4) { case 0: return n; case 1: return 1; case 2: return n + 1; default: return 0; } So you don't actually need the

xor(1..n) = switch(n % 4) { case 0: return n; case 1: return 1; case 2: return n + 1; default: return 0; } So you don't actually need the first loop (at least for the set of integers 1..n example), but bringing that up is probably out of scope for this article.