Odd integers (that is, of the form 2n+1) for which Sum_{i=1..u} J(i,2n+1) obtains value zero exactly 8 times, when u ranges from 1 to (2n+1). Here J(i,k) is the Jacobi symbol.

Of these eight, all are of the form 4k+1, and all others are primes except 65 (= 5*13) and 177 (= 3*59). Conjecture: There are no more terms after the eight one, 193. (Checked up to the 400000th term of A166040, i.e. up to A005408(400000)=800001.)