What are the next three numbers in this sequence?
6, 28, 496, 8128, ... ?
Please explain how you determined these three numbers.
The relation to the Mersenne primes brings to mind that the first four terms of this sequence do not fully identify it. The sequence does in fact show 2^(p1)*(2^p1) for the first four primes. It just happens that for these four primes, 2^p1 is also prime. However, if we choose to continue the series without regard to whether 2^p1 is prime, we get a different continuation:
2 6
3 28
5 496
7 8128
11 2096128
13 33550336
17 8589869056
19 137438691328
23 35184367894528
29 144115187807420416
OK
as produced by the following program:
list
10 P=1
20 for J=1 to 10
30 P=nxtprm(P)
40 print P,2^(P1)*(2^P1)
50 next
so the next three numbers would be 2096128, 33550336, 8589869056, the first of which is imperfect as it does not involve a Mersenne prime.

Posted by Charlie
on 20031130 11:16:54 