REVERSALADDITION
PALINDROME
TEST ON
10548

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 10548: 
10548
+ 84501
step 1: 95049
+ 94059
step 2: 189108
+ 801981
step 3: 991089
+ 980199
step 4: 1971288
+ 8821791
step 5: 10793079
+ 97039701
step 6: 107832780
+ 087238701
step 7: 195071481
+ 184170591
step 8: 379242072
+ 270242973
step 9: 649485045
+ 540584946
step 10: 1190069991
+ 1999600911
step 11: 3189670902
+ 2090769813
step 12: 5280440715
+ 5170440825
step 13: 10450881540
+ 04518805401
step 14: 14969686941
+ 14968696941
step 15: 29938383882
+ 28838383992
step 16: 58776767874
+ 47876767785
step 17: 106653535659
+ 956535356601
step 18: 1063188892260
+ 0622988813601
step 19: 1686177705861
+ 1685077716861
step 20: 3371255422722
+ 2272245521733
step 21: 5643500944455
+ 5544490053465
step 22: 11187990997920
+ 02979909978111
step 23: 14167900976031
+ 13067900976141
step 24: 27235801952172
+ 27125910853272
step 25: 54361712805444
+ 44450821716345
step 26: 98812534521789
+ 98712543521889
step 27: 197525078043678
+ 876340870525791
step 28: 1073865948569469
+ 9649658495683701
step 29: 10723524444253170
+ 07135244442532701
step 30: 17858768886785871


10548 takes 30 iterations / steps to resolve into a 17 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 2,038,048 times since Saturday, March 9^{th}, 2002.)
