[seqfan] Re: A133058

[M. F. Hasler]

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