[seqfan] Re: Prime hatred

Eric Angelini Eric.Angelini at kntv.be
Thu Jan 7 17:24:13 CET 2010

```Many thanks, Robert -- no odd numbers except the starting one...
Please submit and author, if you think this is interesting enough!
Best,
É.

-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu]
De la part de Robert Munafo
Envoyé : jeudi 7 janvier 2010 16:30
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Prime hatred

Okay, after the joke reply and the 37 counterexample, I wrote a program to
calculate the sequence and I get:

1, 8, 6, 10, 14, 12, 4, 20, 16, 24, 18, 22, 28, 26, 34, 30, 32, 36, 40, 42,
46, 38, 44, 52, 48, 54, 50, 58, 56, 62, 64, 60, 66, 68, 72, 70, 74, 80, 76,
78, 86, 82, 84, 90, 92, 94, 88, 98, 96, 104, ...

I am using the definition "The lexicographically first sequence of natural
numbers such that no set of consecutive sequence members adds to a prime,
and no number occurs in the sequence more than once."

If you remove the "no number occurs in the sequence more than once" part, I
get:

1, 8, 6, 6, 4, 8, 6, 6, 4, 6, 8, 6, 6, 6, 4, 6, 4, 4, 6, 6, 4, 4, 4, 6, 4,
8, 4, 8, 6, 6, 4, 6, 8, 4, 8, 6, 4, 4, 4, 4, 4, 4, 6, 4, 8, 4, 6, 6, 6, 8,
...

Neither of these seems to be in OEIS at present.

On Thu, Jan 7, 2010 at 09:49, Eric Angelini <Eric.Angelini at kntv.be> wrote:

>
> Hello SeqFans,
>
> « Build the lexicographically first sequence where no set
>  of consecutive integers sums up to a prime »
>
> I get:
>
> S = 1,8,6,10,12,18,4,14,22,20,16,24,26,...
>
> No prime in S, of course (a one-element set is possible)
>
> Could it be possible that S is a permutation of A018252?
> (the non-prime numbers)
>
> At this point of S there is no odd integer (except "1")...
>

--
Robert Munafo  --  mrob.com

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