A digit reversal property for an analogue of Stern's sequence

TL;DR

This paper proves that a variant of Stern's sequence remains unchanged when the index is replaced by its digit-reversal in base 3, revealing a symmetry property of the sequence.

Contribution

It establishes the digit-reversal invariance property for a specific analogue of Stern's sequence in base 3.

Findings

Sequence is invariant under base-3 digit reversal.

Demonstrates a symmetry property of the sequence.

Provides insight into the structure of Stern-like sequences.

Abstract

We consider a variant of Stern's diatomic sequence, studied recently by Northshield. We prove that this sequence $b$ is invariant under \emph{digit reversal} in base $3$, that is, $b_n=b_{n^R}$, where $n^R$ is obtained by reversing the base-$3$ expansion of $n$.