Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.5

Ternary Modified Collatz Sequences And Jacobsthal Numbers

Ji Young Choi
Department of Mathematics
Shippensburg University of Pennsylvania
1871 Old Main Drive
Shippensburg, PA 17257


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 3N 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.

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(Concerned with sequences A000975 A001045 A005578.)

Received December 23 2015; revised versions received January 7 2016; August 31 2016; September 2 2016. Published in Journal of Integer Sequences, September 7 2016.

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