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 Flawless Series? (Posted on 2003-11-29)
What are the next three numbers in this sequence? 6, 28, 496, 8128, ... ? Please explain how you determined these three numbers.

 See The Solution Submitted by SilverKnight Rating: 2.8889 (9 votes)

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 In fact... (another solution) | Comment 13 of 67 |
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^(p-1)*(2^p-1) for the first four primes. It just happens that for these four primes, 2^p-1 is also prime. However, if we choose to continue the series without regard to whether 2^p-1 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^(P-1)*(2^P-1)
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 2003-11-30 11:16:54

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