[seqfan] Re: Jump and land on a prime

Olivier Gerard olivier.gerard at gmail.com
Fri Dec 23 08:07:44 CET 2011

```Benoit,

as these sequences are not yet in the OEIS, would you please
enter them ?

By the way, are you sure one should describe them as "lexicographically"
ordered and not simply "numerically" ordered as we are not dealing with
a specific base representation ?

Regards,

Olivier

2011/12/22 Benoît Jubin <benoit.jubin at gmail.com>

> This made me think of these two sequences:
>
> * Lexicographically smallest injective sequence of positive integers
> such that a(n+a(n)) is prime for all n.
> 1,2,3,5,4,7,6,8,11,9,10,12,13
>
> * Lexicographically smallest injective sequence of positive integers
> such that a(n) is prime if and only if there is a k such that
> n=k+a(k).
> 1,2,4,3,6,8,5,9,10,12,7,11,14,13
> This is the same if we only ask "a(n) is prime only if there is a k
> such that n=k+a(k)".
>
> * In both sequences, both primes and composites appear in increasing
> order.  These sequences are permutations of the positive integers.
> [note that these sequences correspond to "move to the right by m
> steps", which seems more natural than "jump over p terms" (obviously,
> p=m-1)]
>
> Benoit
>
>
> On Thu, Dec 22, 2011 at 9:30 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
> > Hello SeqFans,
> >
> >
> S=1,2,3,4,5,6,7,8,11,9,13,12,17,10,19,15,23,14,16,29,31,18,20,21,37,22,24,25,26,27,41,43,47,28,53,59,33,30,35,32,61,34,39,67,42,71,44,36,73,79,45,83,89,97,...
> >
> > Pick any S(n) and jump over S(n) terms: you'll land on a Prime.
> > You can jump left or right, it'll do.
> > Examples:
> > "1" leads you to "3" (you have jumped over 1 term)
> > "6" leads you to "17" (you have jumped over 6 terms)
> > "10" leads you to "3" or "37" (you have jumped over 10 terms, left or
> right).
> > S is a permutation of the natural numbers - and the primes appear in
> their natural order.
> > Not sure of the last terms, though.
> > Best,
> > É.
> >
> >
> > _______________________________________________
> >
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>
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>

```