[seqfan] Re: https://oeis.org/A254211 Finite?

Neil Sloane njasloane at gmail.com
Fri Jan 30 00:33:56 CET 2015


MFH's sequence A254337 is very nice.

Could someone please create a b-file, as large as possible,
of course WITHOUT assuming the conjecture is true (that every composite
even number appears and no odd number > 1 appears)?

Is there a simple proof that 9 does not appear?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Thu, Jan 29, 2015 at 12:27 AM, M. F. Hasler <seqfan at hasler.fr> wrote:

> > Am 27.01.2015 um 12:26 schrieb Ron Hardin:
> >> Right, the every partial sum from either end is never prime.
>
> This inspired me https://oeis.org/draft/A254337
>
> Lexicographic first sequence such that a(k)+...+a(n) is never prime
> and all terms are different.
>
> 0, 1, 8, 6, 10, 14, 12, 4, 20, 16, 24, 18, 22, 28, 26, 34, 30, 32, 36,
> 40, 42, ...
>
> The sequence may not contain any prime. Does it contain all even
> numbers > 2? (It seems so.) Does it contain any odd number beyond 1?
> (It seems not.)
>
> (PARI)
> {a=[m=L=u=0];for(i=1,99, print1(a[i]","); u+=2^a[i];
> m==a[i] && while(isprime(m++)||bittest(u,m),); a=concat(a,m);
> until( 0,  s=a[k=i+1]; while( k>1 && ! isprime( s+=a[k--]),);
> isprime(s) || break;while( isprime(a[i+1]++) || bittest(u,a[i+1]),);))}
>
> --
> Maximilian
>
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>



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