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Woodall Number

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A Woodall number is a number of the form

W_n=2^nn-1

for a positive integer n. Woodall numbers are therefore similar to Mersenne numbers 2^n-1 but with an additional factor of n multiplying the power of 2, and to Cullen numbers 2^nn+1 but with the sign flipped.

For n=1, 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.

See also

Cullen Number, Cunningham Number, Fermat Number, Integer Sequence Primes, Mersenne Number, Sierpiński Number of the First Kind, Thābit ibn Qurra Number, Woodall Prime

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References

Cunningham, A. J. C. and Woodall, H. J. "Factorisation of Q=(2^q∓q) and (q·2^q∓1)." 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."

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Woodall Number

Cite this as:

Weisstein, Eric W. "Woodall Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WoodallNumber.html

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