[seqfan] Re: Christmas puzzle: What is the next number in the sequence 2, 3, ...?

[Rainer Rosenthal]

Robert Israel schrieb:
> If p == 1 mod 3, 2p+1 == 0 mod 3.  If p == 2 mod 3, 2p-1 == 0 mod 3.
> So there are no such p > 3.

Well, speaking in the tone of Bill Dubuque:

SIMPLER!
2p-1, 2p, 2p+1 are three numbers in a row. At least one of them has
factor 3, but 2p doesn't have factor 3 for p > 3, p prime.

Friendly greetings and a Happy New Year for you,
Rainer