[seqfan] Re: A168219: No 3 consecutive n's (?)
Maximilian Hasler
maximilian.hasler at gmail.com
Tue Nov 24 16:39:16 CET 2009
of course,
? vector(30,n,10*n^3+1)%3
%7 = [2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1,
2, 0, 1, 2, 0, 1, 2, 0, 1]
i.e. 10*n^3+1 = n+1 (mod 3)
<=> n^3 = n (mod 3)
(Fermat's little thm.)
Maximilian
On Tue, Nov 24, 2009 at 6:08 AM, zak seidov <zakseidov at yahoo.com> wrote:
> %S A168219 1,3,4,6,15,16,18,24,27,30,31,36,37
>
> %N A168219 Naturals n for which 1 + 10*n^3 is prime
>
> %C A168219 (2) It is an open problem if 3 consecutive naturals n exist which give such a prime.
>
> Me: All terms == {0,1} mod 3 => hence no 3 consecutive naturals n can give primes.
>
> I leave rewording and submitA to someone with better math/Eng than me,
>
> Thanks, Zak
>
>
>
>
>
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