Geodesic
Ternary modified Collatz sequences and Jacobsthal numbers
Journal of integer sequences, Tome 19 (2016) no. 7
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},
     year = {2016},
     volume = {19},
     number = {7},
     zbl = {1383.11011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a4/}
}
TY  - JOUR
AU  - Choi,  Ji Young
TI  - Ternary modified Collatz sequences and Jacobsthal numbers
JO  - Journal of integer sequences
PY  - 2016
VL  - 19
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a4/
LA  - en
ID  - JIS_2016__19_7_a4
ER  - 
%0 Journal Article
%A Choi,  Ji Young
%T Ternary modified Collatz sequences and Jacobsthal numbers
%J Journal of integer sequences
%D 2016
%V 19
%N 7
%U http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a4/
%G en
%F JIS_2016__19_7_a4
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/