REVERSAL-ADDITION PALINDROME TEST ON 1036974

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 1036974:
1036974
+ 4796301
step 1: 5833275
+ 5723385
step 2: 11556660
+ 06665511
step 3: 18222171
+ 17122281
step 4: 35344452
+ 25444353
step 5: 60788805
+ 50888706
step 6: 111677511
+ 115776111
step 7: 227453622
+ 226354722
step 8: 453808344
+ 443808354
step 9: 897616698
+ 896616798
step 10: 1794233496
+ 6943324971
step 11: 8737558467
+ 7648557378
step 12: 16386115845
+ 54851168361
step 13: 71237284206
+ 60248273217
step 14: 131485557423
+ 324755584131
step 15: 456241141554
+ 455141142654
step 16: 911382284208
+ 802482283119
step 17: 1713864567327
+ 7237654683171
step 18: 8951519250498
+ 8940529151598
step 19: 17892048402096
+ 69020484029871
step 20: 86912532431967
+ 76913423521968
step 21: 163825955953935
+ 539359559528361
step 22: 703185515482296
+ 692284515581307
step 23: 1395470031063603
+ 3063601300745931
step 24: 4459071331809534
+ 4359081331709544
step 25: 8818152663519078
+ 8709153662518188
step 26: 17527306326037266
+ 66273062360372571
step 27: 83800368686409837
+ 73890468686300838
step 28: 157690837372710675
+ 576017273738096751
step 29: 733708111110807426
+ 624708011111807337
step 30: 1358416122222614763
+ 3674162222216148531
step 31: 5032578344438763294
+ 4923678344438752305
step 32: 9956256688877515599
+ 9955157788866526599
step 33: 19911414477744042198
+ 89124044777441411991
step 34: 109035459255185454189
+ 981454581552954530901
step 35: 1090490040808139985090
+ 0905899318080400940901
step 36: 1996389358888540925991
+ 1995290458888539836991
step 37: 3991679817777080762982
+ 2892670807777189761993
step 38: 6884350625554270524975
+ 5794250724555260534886
step 39: 12678601350109531059861
+ 16895013590105310687621
step 40: 29573614940214841747482
+ 28474714841204941637592
step 41: 58048329781419783385074
+ 47058338791418792384085
step 42: 105106668572838575769159
+ 951967575838275866601501
step 43: 1057074244411114442370660
+ 0660732444111144424707501
step 44: 1717806688522258867078161
+ 1618707688522258866087171
step 45: 3336514377044517733165332
+ 2335613377154407734156333
step 46: 5672127754198925467321665
+ 5661237645298914577212765
step 47: 11333365399497840044534430
+ 03443544004879499356333311
step 48: 14776909404377339400867741
+ 14776800493377340490967741
step 49: 29553709897754679891835482
+ 28453819897645779890735592
step 50: 58007529795400459782571074
+ 47017528795400459792570085
step 51: 105025058590800919575141159
+ 951141575919008095850520501
step 52: 1056166634509809015425661660
+ 0661665245109089054366616501
step 53: 1717831879618898069792278161
+ 1618722979608988169781387171
step 54: 3336554859227886239573665332
+ 2335663759326887229584556333
step 55: 5672218618554773469158221665
+ 5661228519643774558168122765
step 56: 11333447138198548027326344430
+ 03444362372084589183174433311
step 57: 14777809510283137210500777741
+ 14777700501273138201590877741
step 58: 29555510011556275412091655482
+ 28455619021457265511001555592
step 59: 58011129033013540923093211074
+ 47011239032904531033092111085
step 60: 105022368065918071956185322159
+ 951223581659170819560863220501
step 61: 1056245949725088891517048542660
+ 0662458407151988805279495426501
step 62: 1718704356877077696796543969161
+ 1619693456976967707786534078171
step 63: 3338397813854045404583078047332
+ 2337408703854045404583187938333
step 64: 5675806517708090809166265985665
+ 5665895626619080908077156085765
step 65: 11341702144327171717243422071430
+ 03417022434271717172344120714311
step 66: 14758724578598888889587542785741
1036974 takes 66 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 1,768,567 times since Saturday, March 9th, 2002.)