Geodesic
Ternary modified Collatz sequences and Jacobsthal numbers
Journal of integer sequences, Tome 19 (2016) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of $3^{N}$ for an arbitrary large integer $N$. Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is identified as a Jacobsthal number, or one more or one less than a Jacobsthal number.
Classification : 11A67, 11B75
Keywords: Collatz sequence, Collatz problem, Jacobsthal number, ternary representation, 3x + 
@article{JIS_2016__19_7_a4,
     author = {Choi, Ji Young},
     title = {Ternary modified {Collatz} sequences and {Jacobsthal} numbers},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a4/}
}
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Choi, Ji Young. Ternary modified Collatz sequences and Jacobsthal numbers. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a4/