REVERSALADDITION
PALINDROME
TEST ON
989

Reverse and Add Process:
1. Pick a number.
2. Reverse its digits and add this value to the original number.
3. If this is not a palindrome, go back to step 2 and repeat.
 Let's view this Reverse and Add sequence starting with 989: 
989
+ 989
step 1: 1978
+ 8791
step 2: 10769
+ 96701
step 3: 107470
+ 074701
step 4: 182171
+ 171281
step 5: 353452
+ 254353
step 6: 607805
+ 508706
step 7: 1116511
+ 1156111
step 8: 2272622
+ 2262722
step 9: 4535344
+ 4435354
step 10: 8970698
+ 8960798
step 11: 17931496
+ 69413971
step 12: 87345467
+ 76454378
step 13: 163799845
+ 548997361
step 14: 712797206
+ 602797217
step 15: 1315594423
+ 3244955131
step 16: 4560549554
+ 4559450654
step 17: 9120000208
+ 8020000219
step 18: 17140000427
+ 72400004171
step 19: 89540004598


989 takes 19 iterations / steps to resolve into a 11 digit palindrome.

REVERSALADDITION
PALINDROME
RECORDS

Most Delayed Palindromic Number for each digit length
(Only iteration counts for which no smaller records exist are considered.
My program records only the smallest number that resolves for each distinct iteration count.
For example, there are 18digit numbers that resolve in 232 iterations,
higher than the 228 iteration record shown for 18digit numbers, but they were not recorded,
as a smaller [17digit] number already holds the record for 232 iterations.)
Digits  Number  Result 
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

89
187
1,297
10,911
150,296
9,008,299
10,309,988
140,669,390
1,005,499,526
10,087,799,570
100,001,987,765
1,600,005,969,190
14,104,229,999,995
100,120,849,299,260
1,030,020,097,997,900
10,442,000,392,399,960
170,500,000,303,619,996
1,186,060,307,891,929,990

solves in 24 iterations.
solves in 23 iterations.
solves in 21 iterations.
solves in 55 iterations.
solves in 64 iterations.
solves in 96 iterations.
solves in 95 iterations.
solves in 98 iterations.
solves in 109 iterations.
solves in 149 iterations.
solves in 143 iterations.
solves in 188 iterations.
solves in 182 iterations.
solves in 201 iterations.
solves in 197 iterations.
solves in 236 iterations.
solves in 228 iterations.
solves in 261 iterations  World Record!

[View all records] 
This reverse and add program was created by Jason Doucette.
Please visit my Palindromes and World Records page.
You have permission to use the data from this webpage (with due credit). A link to my website is much appreciated. Thank you.
(This program has been run 1,886,779 times since Saturday, March 9^{th}, 2002.)
