Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.3 |

University of North Dakota

Department of Mathematics

Witmer Hall Room 313

101 Cornell Street Stop 8376

Grand Forks, ND 58202-8376

USA

**Abstract:**

For an integer and for
, define
,
where
denotes the fractional part of the real number .
A number of
properties of are derived, and then a connection between and the rumor
conjecture is established. To form a rumor sequence , first select integers
and . Then
select an integer , and for let
, where the right
side is the least non-negative residue of modulo . The rumor sequence
conjecture asserts that all such rumor sequences are eventually 0. A condition on
is shown to be equivalent to the rumor conjecture.

(Concerned with sequences A049802 A049803 A080277 A080333 A177356 .)

Received December 1 2010;
revised version received February 1 2011.
Published in *Journal of Integer Sequences*, February 19 2011.

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