Geodesic
A Tribonacci-like sequence of composite numbers
Journal of integer sequences, Tome 20 (2017) no. 3
We find a new Tribonacci-like sequence of positive integers 〈 $x_{0}, x_{1}, x_{2}, \dots $〉 given by $x_{n} = x_{n-1} + x_{n-2} + x_{n-3}, n \ge 3$, and $gcd(x_{0},x_{1},x_{2}) = 1$ that contains no prime numbers. We show that the sequence with initial values $x_{0} = 151646890045, x_{1} = 836564809606, x_{2} = 942785024683$ is the current record in terms of the number of digits.
Keywords: tribonacci-like recurrence, composite number 
@article{JIS_2017__20_3_a4,
     author = {Lunev,  Ivan},
     title = {A {Tribonacci-like} sequence of composite numbers},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {3},
     zbl = {1381.11013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a4/}
}
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%J Journal of integer sequences
%D 2017
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Lunev,  Ivan. A Tribonacci-like sequence of composite numbers. Journal of integer sequences, Tome 20 (2017) no. 3. http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a4/