REVERSAL-ADDITION PALINDROME TEST ON 1009227

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 1009227:
1009227
+ 7229001
step 1: 8238228
+ 8228328
step 2: 16466556
+ 65566461
step 3: 82033017
+ 71033028
step 4: 153066045
+ 540660351
step 5: 693726396
+ 693627396
step 6: 1387353792
+ 2973537831
step 7: 4360891623
+ 3261980634
step 8: 7622872257
+ 7522782267
step 9: 15145654524
+ 42545654151
step 10: 57691308675
+ 57680319675
step 11: 115371628350
+ 053826173511
step 12: 169197801861
+ 168108791961
step 13: 337306593822
+ 228395603733
step 14: 565702197555
+ 555791207565
step 15: 1121493405120
+ 0215043941211
step 16: 1336537346331
+ 1336437356331
step 17: 2672974702662
+ 2662074792762
step 18: 5335049495424
+ 4245949405335
step 19: 9580998900759
+ 9570098990859
step 20: 19151097891618
+ 81619879015191
step 21: 100770976906809
+ 908609679077001
step 22: 1009380655983810
+ 0183895560839001
step 23: 1193276216822811
+ 1182286126723911
step 24: 2375562343546722
+ 2276453432655732
step 25: 4652015776202454
+ 4542026775102564
step 26: 9194042551305018
+ 8105031552404919
step 27: 17299074103709937
+ 73990730147099271
step 28: 91289804250809208
+ 80290805240898219
step 29: 171580609491707427
+ 724707194906085171
step 30: 896287804397792598
+ 895297793408782698
step 31: 1791585597806575296
+ 6925756087955851971
step 32: 8717341685762427267
+ 7627242675861437178
step 33: 16344584361623864445
+ 54446832616348544361
step 34: 70791416977972408806
+ 60880427977961419707
step 35: 131671844955933828513
+ 315828339559448176131
step 36: 447500184515382004644
+ 446400283515481005744
step 37: 893900468030863010388
+ 883010368030864009398
step 38: 1776910836061727019786
+ 6879107271606380196771
step 39: 8656018107668107216557
+ 7556127018667018106568
step 40: 16212145126335125323125
+ 52132352153362154121261
step 41: 68344497279697279444386
1009227 takes 41 iterations / steps to resolve into a 23 digit palindrome.

REVERSAL-ADDITION 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 18-digit numbers that resolve in 232 iterations, higher than the 228 iteration record shown for 18-digit numbers, but they were not recorded, as a smaller [17-digit] number already holds the record for 232 iterations.)

DigitsNumberResult
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 2,549,890 times since Saturday, March 9th, 2002.)