[seqfan] Re: A133058

[Allan Wechsler]

A comment by the author (Zizka) seems to recognize the possibility of these
period-4 regimes. This leads me to think that one might devise a
meta-sequence telling how soon the regime is entered depending on starting
values.
On Feb 15, 2015 9:05 AM, "M. F. Hasler" <oeis at hasler.fr> wrote:

> On Sat, Feb 14, 2015 at 7:51 PM, Allan Wechsler <acwacw at gmail.com> wrote:
> > If the program and b-file are right, the sequence enters a very simple
> > regime at n=638.
> > a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2,
> for
> > all k>=0.
>
> I agree with Allan's result (and added PARI code producing the same
> sequence).
> If one defines
> a(1)=1; a(n+1) = a(n) + n + 1 if a(n) and n are coprime,
> otherwise a(n+1) = a(n)/gcd(a(n),n).
>
> one gets a "trivial" sequence having this behaviour right from the start :
>  1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19,...
> i.e., a(4n+1) = 1, a(4n+2) = 4n+3, a(4n+3) = 8n+6, a(4n) = 2.
>
> which I submitted in spite of "kw: easy, dumb" as A255051 ;
> Changing the +1 to +2  yields yet another (less trivial) variant,
> 1, 4, 2, 7, 13, 20, 10, 19, 29, 40, 4, 17, 31, 46, 23, 40, 5, ...
> submitted as A255140.
> --
> Maximilian
>
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