[math-fun] Skolem-like primes sequence

[Richard Guy]

It might be nearer to the original
Langford-Skolem idea, only to have 2
occurrences of each prime:

2 3 5 2 7 3 11 13 5 17 19 23 7 29 31 37 41 43 11 47 ...
if you do this with natural numbers instead of
primes you get  A026272.

The usual generalization is to 3, 4, ...
occurrences.  With the natural numbers
you run into trouble.  Either put each number
in its earliest possible three positions:

1 . 1 2 1 6 2 3 4 2 5 3 6 4 8 3 5 7 4 6 9 . 5 8
     10 7 11 . 12 . 9 13 8 7 . 10 . . 11 . 9 12

(if I've got it right -- or even if I haven't)
and it's not clear that the holes will eventually
get filled ... .
Or, put the earliest numbers in the available
positions:

1 3 1 4 1 3 5 6 4 3 7 5 9 4 6 8 5 2 7 10 2 6 9 2
      8 11 7 . . . 10 . 9 8 . . . 11 . . . 10 .

and I thought that  2  wasn't going to make it --
will all the numbers find a place?

4, 5, ... occurrences left to the reader.  R.

On Mon, 18 Sep 2006, Eric Angelini wrote:

> Hello SeqFans and Math-Fun,
> is this of interest?
> best,
> É.
> http://www.cetteadressecomportecinquantesignes.com/SkolemPrimes.htm
>
>
>
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