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Long(infinite?) way to create a palindrome (Posted on 2012-11-04) Difficulty: 3 of 5
The Palindromic Number Conjecture states that: All integers will eventually produce a palindromic number if the following-algorithm is repeatedly applied to them:
Take an integer, reverse its digits and add it to itself,
it quickly becomes a palindromic number, that is, the digits are the same forwards and backward.
For example, start with 97:
97 + 79 = 176
176 + 671 = 847
847 + 748 = 1585
1585 + 5851 = 7546
7546 + 6457 = 14003
14003 + 30041 = 44044 ...done...
The conjecture has not been proven or found false for all integers in their base ten form.
Normally, the integers become palindromes quickly - until you get to x.

Find x.

Source: appears in several textbooks, papers and curios' collections.

See The Solution Submitted by Ady TZIDON    
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Solution an answer | Comment 1 of 2
If I have not erred, the first number in which the number of algorithmic iterations seems infinitely high in number is 196.

After posting the above answer, I Googled the "Palindromic Number Conjecture". It is indeed the first of 5996 of 100,000 numbers that never seem to generate a palindromic number. It also lends itself to the name for the algorithm as the 196-algorithm. The first few following 196 are 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, ... (Sloane's A006960).

Edited on November 4, 2012, 11:43 am
  Posted by Dej Mar on 2012-11-04 11:35:56

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