Look and Say Sequence

Source: Attributed to Conway.

[Spoiler Alert] The problem is adapted from the Green Chicken Problems - November 15, 2014 – 36th Competition.

Conway’s see-and-say (or the look-and-say) sequence has fascinated people for years, and is a fun, non-standard example of a sequence. Starting with $a_1 = 1$, we define $a_{n+1}$ as the sequence obtained by saying the previous sequence aloud. The first few terms are 1, 11 (one one), 21 (two ones), 1211 (one two, one one), 111221 (one one, one two, two ones), 312211 (three ones, two twos, one one).

We observe that the largest number in the 2023th term of this sequence is a 7, and coincidentally, 2023 is the 7th year of the Btech program in CSE at IITGN. This coincidence makes us very happy.

However, is our observation correct?