# Fibonacci-Like Sequence With Mod

Franklin T. Adams-Watters franktaw at netscape.net
Thu Jun 24 01:02:30 CEST 2004

```franktaw at netscape.net (Franklin T. Adams-Watters) wrote:

>Leroy Quet <qq-quet at mindspring.com> wrote:
>
>>Let a(0) = a(1) = 1;
>>
>>Let, for 2 <= m,
>>
>>a(m) = a(m-1) + a(m-2) (mod m),
>
>1,1,0,1,1,2,3,5,0,5,5,10,3,0,3,3,6,9,15,5,0,5,5,10,15,0,15,15,2,17,...
>
>I looked at sequences of this type several years ago.  To me, this is not the most natural such sequence; I would start with a(1) = 0 and a(2) = 1, giving us:
>
>0,1,1,2,3,5,1,6,7,3,10,1,11,12,8,4,12,16,9,5,14,19,10,5,15,20,8,0,8,...
>
>My second choice would be to start with a(0) = 0 and a(1) = 1, which gives:
>
>0,1,1,2,3,0,3,3,6,0,6,6,0,6,6,12,2,14,16,11,7,18,3,21,0,21,21,15,8,...
>
>This sequence is in the OEIS, as A079777.  The other two are not.

I have now submitted the other two.

>The basic question about these sequences is the truth of the conjecture that every integer occurs (infinitely often) in such a sequence.

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