Aaaarrggghhh ... mistake in the third sequence below: On Mon, 18 Sep 2006, Richard Guy wrote:
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: x 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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