Definition:Woodall Prime/Sequence

Sequence

The sequence $\sequence n$ for which $n \times 2^n - 1$ is a prime number begins:

$2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, \ldots$

This sequence is A002234 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

The first few of these correspond with the sequence $\sequence n$ of the actual Woodall primes themselves, which begins:

$7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, \ldots$

This sequence is A050918 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

This article is complete as far as it goes, but it could do with expansion. In particular: Use a format similar to that of Mersenne Primes. Set up templates for the construction of such a table, and use it as the basis of similar tabular constructions. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $141$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $141$

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