A Tribonacci-Like Sequence of Composite Numbers
Department of Mathematics and Mechanics
Saint-Petersburg State University
28 Universitetsky Prospect
St. Petersburg, 198504
We find a new Tribonacci-like sequence of positive
integers ⟨ x0, x1, x2, ... ⟩
given by xn = xn-1
+ xn-2 + xn-3,
n ≥ 3,
and gcd(x0,x1,x2) = 1 that
contains no prime numbers. We show that the sequence with initial
values x0 = 151646890045, x1 = 836564809606, x2 = 942785024683 is the
current record in terms of the number of digits.
Full version: pdf,
(Concerned with sequences
Received November 20 2016; revised versions received November 25 2016; December 27 2016;
January 3 2017.
Published in Journal of Integer Sequences, January 3 2017.
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