[ July 27, 2003 ] [ Last update May 24, 2024 ]
Expressions with a palindromic look

Here is an expression that I wrote down a while ago.
When you consider only its digits you'll notice
that we deal here with a palindrome ie, 3233223323.

(3^2)^3 + ((3^2)2)^3 = 3^(2^3)

equivalent to 729 + 5832 = 6561 or 9³ + 18³ = 3⁸.

A neat fact published in newsgroup sci.math.
and announced as a " multi-palindromic bi-digital curiosity ".
by Don Mcdonald dd. Sep 29 1996.

Exist there other non-trivial expressions possessing such a
beautiful palindromic (symmetrical) look regarding its digits ?

The 37^th Mersenne Prime
2^3021377 – 1
has a prime exponent that can be rewritten
as a palindromic expression in the following manner

3021377 = 1 * 2 * 34 * 44432 + 1

and 1234444321 is a beautiful palindromic number.
A neat fact published in newsgroup rec.puzzles
makes this "an easy to remember mersenne prime ".
also by Don Mcdonald dd. May 15 2000.

Some examples with powers

2⁴ = 4²

1 * 8²⁸ = 8 * 2⁸¹

46 * 22² = 22264

81⁹ = 9¹⁸

1 * 2⁹²² = 2 * 2⁹²¹

(1 + 4)² = 24 + 1

Some examples with only multiplication

21 * 6 = 612

51 * 3 = 315

86 * 8 = 868

4307 * 62 = 267034

5322 * 42 = 242235

20781 * 9 = 918702