REVERSAL-ADDITION PALINDROME TEST ON 1003569

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 1003569:
1003569
+ 9653001
step 1: 10656570
+ 07565601
step 2: 18222171
+ 17122281
step 3: 35344452
+ 25444353
step 4: 60788805
+ 50888706
step 5: 111677511
+ 115776111
step 6: 227453622
+ 226354722
step 7: 453808344
+ 443808354
step 8: 897616698
+ 896616798
step 9: 1794233496
+ 6943324971
step 10: 8737558467
+ 7648557378
step 11: 16386115845
+ 54851168361
step 12: 71237284206
+ 60248273217
step 13: 131485557423
+ 324755584131
step 14: 456241141554
+ 455141142654
step 15: 911382284208
+ 802482283119
step 16: 1713864567327
+ 7237654683171
step 17: 8951519250498
+ 8940529151598
step 18: 17892048402096
+ 69020484029871
step 19: 86912532431967
+ 76913423521968
step 20: 163825955953935
+ 539359559528361
step 21: 703185515482296
+ 692284515581307
step 22: 1395470031063603
+ 3063601300745931
step 23: 4459071331809534
+ 4359081331709544
step 24: 8818152663519078
+ 8709153662518188
step 25: 17527306326037266
+ 66273062360372571
step 26: 83800368686409837
+ 73890468686300838
step 27: 157690837372710675
+ 576017273738096751
step 28: 733708111110807426
+ 624708011111807337
step 29: 1358416122222614763
+ 3674162222216148531
step 30: 5032578344438763294
+ 4923678344438752305
step 31: 9956256688877515599
+ 9955157788866526599
step 32: 19911414477744042198
+ 89124044777441411991
step 33: 109035459255185454189
+ 981454581552954530901
step 34: 1090490040808139985090
+ 0905899318080400940901
step 35: 1996389358888540925991
+ 1995290458888539836991
step 36: 3991679817777080762982
+ 2892670807777189761993
step 37: 6884350625554270524975
+ 5794250724555260534886
step 38: 12678601350109531059861
+ 16895013590105310687621
step 39: 29573614940214841747482
+ 28474714841204941637592
step 40: 58048329781419783385074
+ 47058338791418792384085
step 41: 105106668572838575769159
+ 951967575838275866601501
step 42: 1057074244411114442370660
+ 0660732444111144424707501
step 43: 1717806688522258867078161
+ 1618707688522258866087171
step 44: 3336514377044517733165332
+ 2335613377154407734156333
step 45: 5672127754198925467321665
+ 5661237645298914577212765
step 46: 11333365399497840044534430
+ 03443544004879499356333311
step 47: 14776909404377339400867741
+ 14776800493377340490967741
step 48: 29553709897754679891835482
+ 28453819897645779890735592
step 49: 58007529795400459782571074
+ 47017528795400459792570085
step 50: 105025058590800919575141159
+ 951141575919008095850520501
step 51: 1056166634509809015425661660
+ 0661665245109089054366616501
step 52: 1717831879618898069792278161
+ 1618722979608988169781387171
step 53: 3336554859227886239573665332
+ 2335663759326887229584556333
step 54: 5672218618554773469158221665
+ 5661228519643774558168122765
step 55: 11333447138198548027326344430
+ 03444362372084589183174433311
step 56: 14777809510283137210500777741
+ 14777700501273138201590877741
step 57: 29555510011556275412091655482
+ 28455619021457265511001555592
step 58: 58011129033013540923093211074
+ 47011239032904531033092111085
step 59: 105022368065918071956185322159
+ 951223581659170819560863220501
step 60: 1056245949725088891517048542660
+ 0662458407151988805279495426501
step 61: 1718704356877077696796543969161
+ 1619693456976967707786534078171
step 62: 3338397813854045404583078047332
+ 2337408703854045404583187938333
step 63: 5675806517708090809166265985665
+ 5665895626619080908077156085765
step 64: 11341702144327171717243422071430
+ 03417022434271717172344120714311
step 65: 14758724578598888889587542785741
1003569 takes 65 iterations / steps to resolve into a 32 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 1,703,620 times since Saturday, March 9th, 2002.)