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My favourite palindrome

Allow me to show you one of my most favourite palindromic numbers
323323
Why ? Because it can be expressed as the result of some remarkable and unrelated operations.

323323 7 x 11 x 13 x 17 x 19
Product of 5 successive primes A046303
Palindromes with exactly 5 distinct prime factors A046395
17 + 22 + 38 + 49 + 55 + 66 + 71 + 84 + 93
323323 is a substring of its base 4 representation 1032{323323}.
a(n) is substring of its base 4 representation A038104
The string 323323 was found at position 985589 counting
from the first digit after the decimal point of Pi. [ Pi-Search Page ]
First location of palindrome a(n) in Pi is palindromic A038101
Occurs in the curious palindrome products (detected by Hugo Sánchez)
of prime 333667 with palindromic pattern 6(3)n6 with n equal to 4 :
333667 * 633336 = 211{323323}112
Note that 211 added to 112 gives 323 again !

The first is as the product of  five consecutive primes !
The second as a sum of the nine digits (p.2) 1 through 9 [ 123456789 ] each raised to a power.
The different exponents thereby forming a combination of these same nine digits ! [ 728956143 ]
The third and the fourth are self-explanatory...

A000052 Prime Curios! Prime Puzzle
Wikipedia 52 Le Nombre 52 Numberland 52














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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com