Quote:
Originally Posted by GP2
Never mind larger examples, there's no smaller example.
The only other p=2^k+k which is a Mersenne prime exponent is k=1, p=3, but then W(k) = 1.

Not sure I know what you mean. With k=1 you are describing the smaller example. It gives \(2^k+k = 3\) and \(2^k=2\) and the prime (seven) is \[M(3)=2^31=2\cdot 2^2  1=W(2)\]
The other example k=9 written the same way, since \(2^k+k = 521\) and \(2^k=512\), is \[M(521)=2^{521}1=512\cdot 2^{512}  1=W(512)\]
For the fun of it, we can merge the lists of Mersennes and Woodalls like this:
Code:
M(2)
M(3) = W(2)
W(3)
M(5)
M(7)
W(6)
M(13)
M(17)
M(19)
M(31)
W(30)
M(61)
W(75)
W(81)
M(89)
M(107)
W(115)
M(127)
W(123)
W(249)
W(362)
W(384)
W(462)
M(521) = W(512)
M(607)
W(751)
W(822)
M(1279)
M(2203)
M(2281)
M(3217)
M(4253)
M(4423)
W(5312)
. .
. .
. .