Woodall Number

A Woodall number is a number of the form

Woodall numbers are therefore similar to Mersenne numbers  but with an additional factor of  multiplying the power of 2, and to Cullen numbers  but with the sign flipped.

For , 2, ..., the first few Woodall numbers are 1, 7, 23, 63, 159, 383, ... (OEIS A003261).

A Woodall number that is prime is known as a Woodall prime.

REFERENCES:

Cunningham, A. J. C. and Woodall, H. J. "Factorisation of  and ." Messenger Math. 47, 1-38, 1917.

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 360-361, 1996.

Sloane, N. J. A. Sequence A003261/M4379 in "The On-Line Encyclopedia of Integer Sequences."