Journal of Integer Sequences, Vol. 24 (2021), Article 21.3.3

Complementary Equations with Advanced Subscripts

Clark Kimberling
Department of Mathematics
University of Evansville
Evansville, IN 47722

Peter J. C. Moses
Engineering Division, Moparmatic Co.
Astwood Bank, Nr. Redditch
Worcestershire, B96 6DT


This paper discusses complementary equations, such as an = bn + b2n, in which (an) and (bn) are strictly increasing complementary sequences for which, in addition to the subscript n, at least one subscript in advance of n, such as n + 1 or 2n, occurs. Some of the equations are solved with proofs, and others are presented as conjectures or examples based on Mathematica programs that appear in the final section of the paper.

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(Concerned with sequences A000201 A001500 A304799 A304800 A304801 A304802 A304803 A304804 A304805 A304806 A304807 A304808 A304809 A304810 A304811 A304812 A304813 A304814 A304815 A304816 A309156 A326661.)

Received December 2 2020; revised version received February 6 2021. Published in Journal of Integer Sequences, February 6 2021.

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