A Woodall number has the form \(W_k = k \cdot 2^k - 1\) — the Cullen form with the sign flipped. The sequence: 1, 7, 23, 63, 159, 383, 895, 2047, 4607.
Named for H. J. Woodall, who studied them in 1917 alongside Allan Cunningham (of the Cunningham Project, the long-running effort to factor numbers of special forms). Woodall primes (\(k\) = 2, 3, 6, 30, 75, 81, 115, …) are rare, and like Cullen primes are conjectured to be infinite but proven nothing of the sort.