196-Algorithm
Take any Positive Integer of two Digits or more, reverse the Digits, and add tothe original number. Now repeat the procedure with the Sum so obtained. This procedure quickly producesPalindromic Numbers for most Integers. For example, starting with the number5280 produces (5280, 6105, 11121, 23232). The end results of applying the algorithm to 1, 2, 3, ... are 1, 2, 3, 4, 5, 6,7, 8, 9, 11, 11, 33, 44, 55, 66, 77, 88, 99, 121, ... (Sloane's A033865). The value for 89 is especially large, being8813200023188.
The first few numbers not known to produce Palindromes are 196, 887, 1675, 7436,13783, ... (Sloane's A006960), which are simply the numbers obtained by iteratively applying the algorithm to thenumber 196. This number therefore lends itself to the name of the Algorithm.
The number of terms 
in the iteration sequence required to produce a Palindromic Number from 
(i.e., 
for a Palindromic Number, 
if a Palindromic Number is produced after asingle iteration of the 196-algorithm, etc.) for 
, 2, ... are 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2,2, 2, 2, 2, 3, 2, 2, 1, ... (Sloane's A030547). The smallest numbers which require 
, 1, 2, ... iterations toreach a palindrome are 0, 10, 19, 59, 69, 166, 79, 188, ... (Sloane's A023109).
References
Gardner, M. Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American. New York: Knopf, pp. 242-245, 1979. Gruenberger, F. ``How to Handle Numbers with Thousands of Digits, and Why One Might Want to.'' Sci. Amer. 250, 19-26, Apr. 1984. Sloane, N. J. A. Sequences A023109,A030547,A033865, andA006960/M5410in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Augend
- Augmented Amicable Pair
- Augmented Dodecahedron
- Augmented Hexagonal Prism
- Augmented Pentagonal Prism
- Augmented Polyhedron
- Augmented Sphenocorona
- Augmented Triangular Prism
- Augmented Tridiminished Icosahedron
- Augmented Truncated Cube
- Augmented Truncated Dodecahedron
- Augmented Truncated Tetrahedron
- Aureum Theorema
- Aurifeuillean Factorization
- Ausdehnungslehre
- Authalic Latitude
- Autocorrelation
- Automorphic Function
- Automorphic Number
- Automorphism
- Automorphism Group
- Autonomous
- Autoregressive Model
- Auxiliary Circle
- Auxiliary Latitude