TITLE: Why is Sesame Street's Count von Count's favorite number $34,\!969$?
QUESTION [19 upvotes]: In the 2 minute BBC News audio clip Sesame Street: What is Count von Count's favourite number? "The Count" is asked

Do you have a favorite number?

to which he replied

Thirty four thousand, nine hundred and sixty nine. It's a square root thing.

Does the number 34,969 have any particularly notable properties that would make it "The Count"'s favorite number?



Revelations from the world of counting from the late Jerry Nelson, the voice of Count von Count, who was interviewed by Tim Harford to mark Sesame Street's 40th anniversary in 2009.
Photo: Count von Count attends Macy's Thanksgiving Parade 2018 Credit: Getty Images
Release date: 01 February 2019
Duration: 2 minutes

REPLY [4 votes]: Presumably if it's a square root thing, we're allowed to consider its square root, which, as other answers have noted, is $187$.
According to David Wells, The Penguin Dictionary of Curious and Interesting Numbers, (Penguin, 1986), $187$ is

The smallest of a group of $3$-digit numbers that require $23$ reversals to form a palindrome.

This is then followed by the entry for $196$, which includes an explanation of palindromes by reversal. The procedure is to reverse a number's digits and add the resulting number to the original.

Do all numbers become palindromes eventually? The answer to this problem is not known. $196$ is the only number less than $10,000$ that by this process has not yet produced a palindrome. P. C. Leyland has performed $50,000$ reversals, producing a number of more than $26,000$ digits with no palindrome appearing, and P. Anderton has taken this up to $70,928$ digits, also without success.

Most of the $3$-digit numbers require only a few reversals. The ones needing $23$ are
$$\{187, 286, 385, 583, 682, 781, 880\},$$
all of which go via $968$ then $1837$, and end up at $8813200023188$.
So my guess is that the Count is able to take the square root of $34969$ in his head then do the $23$ reversals and get the palindrome, but hasn't yet managed to do the same with $38416=196^2$.