[seqfan] Add-if-odd sequence
zakseidov at yahoo.com
Sat Dec 26 17:08:37 CET 2009
Subj: Add-if-odd sequence
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:
with cycle 0, and the next term is 0.
At a(1)=5, the sequence is:
with cycle 9,18, and the next term is 9.
At a(1)=1711, the sequence is:
with cycle 1791,1809,1827,1845,1863,1881,1899,1926,
and the next term is 1791.
At a(1)=10810065, the sequence is:
with cycle 10810044,10810026,10810008,10809990,10809954,
and the next term is 10810044.
Merry Christmas and happy New Year to ALCORN!
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