# [seqfan] Re: Ratio-Related Sequence: Permutation Of +Integers?

Prof. Dr. Alois Heinz heinz at hs-heilbronn.de
Thu May 7 02:41:31 CEST 2009

```This sequence looks very interesting.

I have computed the first 130000 elements.
a(130000) =  24821868931413592736277574556762175

Still missing:
19, 23, 27, 29, 31, 32, 37, 38, 41, 43, 45, 46, 47, 53, 54, 57, 58, 59,
61, 62, 64, ...

Largest element so far:
3849674323423933173377195599207667400589234486050

I would not bet that every positive integer will occur.
But at the moment I do not see any proof.

Alois

Leroy Quet schrieb:

>I just submitted this (and A160257).
>
>Is this sequence a permutation of the positive integers?
>(By definition, no terms occurs more than once in the sequence. But does every term occur? I bet they do, but maybe the primes don't all necessarily occur.)
>
>%I A160256
>%S A160256 1,2,3,4,6,8,9,16,18,24,12,10,30,5,36,15,48
>%N A160256 a(1)=1, a(2)=2. For n >=3, a(n) = the smallest positive integer not occurring earlier in the sequence such that a(n)*a(n-1)/a(n-2) is an integer.
>%C A160256 Is this sequence a permutation of the positive integers?
>%C A160256 a(n+2)*a(n+1)/a(n) = A160257(n).
>%Y A160256 A075075,A160257
>%K A160256 more,nonn
>%O A160256 1,2
>
>Also, in the related sequence A075075 (same as this sequence, except that the ratio a(n)*a(n-2)/a(n-1) is an integer), it states that that sequence is a permutation of the positive integers. Is this a fact?
>
>Thanks,
>Leroy Quet
>
>

```