Abstract

The digital time group $T_G$, defined by one of us KSR (with Pankaj Pundir) [1] has three two-digit fields for its elements: $h_2h_1 : m_2m_1 : s_2s_1$ and is identified with appropriate restricted place values on the hours (H), minutes (M) and seconds (S) fields. It is an 86,400-element Digital Time group, $T_G$. In this note it is shown that there exists a time-ordered sequence of 125 palindromic elements, as a subset of the group $T_G$, starting with 1:11:11 (interpreting, for example, 1:23:21 which without the semicolons, is 12321, a palindromic number, which reads the same when read from left to right or right to left), ending with 5:55:55 which gives rise to a new hierarchy of palindromic sequences.

Keywords and Phrases

Analytic Number Theory, sequences, palindromic sequences, digital time group, Digital Time, Finite Group, Finite Field, Order of Elements, Palindromic sequences.

A.M.S. subject classification

05C25, 20F65.

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