Journal of Integer Sequences, Vol. 19 (2016), Article 16.3.1

New Integer Sequences Arising From 3-Period Folding Numbers

Quynh Nguyen, Jean Pedersen, and Hien T. Vu
Department of Mathematics and Computer Science
Santa Clara University
Santa Clara, CA 95053


Following Pólya's "guess and test" method, we seek to discover 3-period folding numbers analogous to the exhaustive set of 2-period folding numbers discovered by Hilton and Pedersen in 1981. Most of the rows and columns of the 2-period folding numbers are reported in the Online Encyclopedia of Integer Sequences (OEIS) with various other mathematical interpretations. We provide a table of 3-period folding numbers, but it is not exhaustive, as we demonstrate by showing other sets of 3-period folding numbers that are not in the table. We close the paper with an algorithm for finding more sets of 3-period folding numbers and a conjecture about how many such sets exist.

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(Concerned with sequences A000225 A002450 A007583 A020514 A020515 A020516 A020518 A020519 A020521 A023001 A034496 A034665 A034674 A083318 A131865 A132469 A133853 A135576 A218723.)

Received April 10 2013; revised versions received December 30 2013; January 23 2016; February 6 2016. Published in Journal of Integer Sequences, March 19 2016.

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