Jim Nastos nastos at gmail.com
Sat Dec 26 18:26:49 CET 2009

```I confirm cycles for all starting points up to 150 million. In
general, very short trajectories and short period cycles throughout.
I'll compute up to 250million... if I don't send another message, you
can assume I didn't find a non-cycling trajectory up to 250 million.
J

On Sat, Dec 26, 2009 at 8:08 AM, zak seidov <zakseidov at yahoo.com> wrote:
>
> Dear seqfans,
>
> Does the sequence defines by recurrence
> a(n+1)=a(n)+/-sd(a(n)), if  a(n) is odd/even,
> with sd(m)=sum of digits of m,
> end in cycle for any initial a(1)?
>
> Here are 4 examples with cycles of various lengths.
>
> At a(1)=1, the sequence is:
> 1,2,0,0,0,0,0,0
> with cycle 0, and the next term is 0.
>
> At a(1)=5, the sequence is:
> 5,10,9,18,9,18,9,18
> with cycle 9,18, and the next term is 9.
>
> At a(1)=1711, the sequence is:
> 1711,1721,1732,1719,1737,1755,1773,1791,1809,1827,1845,1863,1881,1899,1926,1908,1890,1872,1854,1836,1818,1800,1791,1809,1827,1845,1863,1881,1899,1926
> with cycle 1791,1809,1827,1845,1863,1881,1899,1926,
>  1908,1890,1872,1854,1836,1818,1800,
> and the next term is 1791.
>
> At a(1)=10810065, the sequence is:
> 10810065,10810086,10810062,10810044,10810026,10810008,10809990,10809954,10809918,10809882,10809846,10809810,10809783,10809819,10809855,10809891,
> 10809927,10809963,10809999,10810044,10810026,10810008,10809990,10809954,
>  with cycle   10810044,10810026,10810008,10809990,10809954,
> 10809918,10809882,10809846,10809810,10809783,10809819,10809855,10809891,10809927,10809963,10809999,
> and the next term is 10810044.
>
> Merry Christmas and happy New Year to ALCORN!
> Zak
>
>
>
>
>
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>

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