Saippuakauppias
Clifford A Pickover · 2001
Abstract In this chapter Dr. Googol is more interested in palindromic numbers than palindromic words or sentences. Palindromic numbers are positive integers that “read” the same backward or forward. For example, 12,321, 11, 261162, and 454 are all palindromic numbers. Figure 57.1 is an interesting plot showing the distribution of the first 200 palindromes when multiplied by a constant. To create the plot, start with an integer x between 1 and 200, multiply it by a constant a, and determine if the result is a palindrome. The “multiplier” a on the y axis of the plot goes from 1 to 200. A dot on the graph indicates a palindromic number. The various patterns produced are quite interesting, and Dr. Googol is fond of making a few casual observations. Note that there is clearly a dense structure below some “hyperbolic” boundary. There is a conspicuous vertical line of closely spaced dots at x = 55 corresponding to 10 consecutive odd a values that produce palindromes. The products are 55 x 91, 55 × 93, 55 × 95, 55 × 97, 55 × 99, 55 × 101, 55 × 103, 55 × 105, 55 × 107, and 55 × 109. Also, when the x-axis value is an even multiple of 5, there are no y data. When the x-axis value is a nonpalindromic odd multiple of 5, they data are scarce. When x is palindromic, there are many y-data points. Notice the plot has symmetry: if x × y is palindromic, y × x is also palindromic.