196 (number)

196 is a natural number following 195 and preceding 197. It is the square of 14. In addition to being a square number, it is also an 11-gonal number, a 34-gonal number, a heptagonal pyramidal number, and a pentagonal pyramidal number.

196 is also the second number "n" for which the sum of the prime factors of 2"n"-1 is twice the sum of the prime factors of ½"n"+1.

Since it is possible to find sequences of 196 consecutive integers such that each inner member shares a factor with either the first or the last member, 196 is an Erdős–Woods number.

According to a conjecture, 196 is the lowest Lychrel number candidate, or the lowest number which is not known to produce a palindromic number by reversal and addition of the digits. For example, if you add 106 to the reverse of its digits, 601, you get 707, which is a palindrome. But with 196, you get 196 + 691 = 887, which is not a palindrome. Neither is 887 + 788 = 1675. This operation has been repeated almost 700 million times without finding a palindrome, but no one has ever proven that it will never produce one.

In other fields

*Interstate 196 is a long spur route of Interstate 96 in Michigan.
*The year 196.

References

* Wells, D. (1987). "The Penguin Dictionary of Curious and Interesting Numbers" (pp. 142 - 143). London: Penguin Group.

External links

* [http://www.p196.org 196 and Other Lychrel Numbers]
* [http://www.jasondoucette.com/worldrecords.html Jason Doucette - World Records, 196 Palindrome Quest]