REVERSAL-ADDITION PALINDROME TEST ON 10833

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 10833:
10833
+ 33801
step 1: 44634
+ 43644
step 2: 88278
+ 87288
step 3: 175566
+ 665571
step 4: 841137
+ 731148
step 5: 1572285
+ 5822751
step 6: 7395036
+ 6305937
step 7: 13700973
+ 37900731
step 8: 51601704
+ 40710615
step 9: 92312319
+ 91321329
step 10: 183633648
+ 846336381
step 11: 1029970029
+ 9200799201
step 12: 10230769230
+ 03296703201
step 13: 13527472431
+ 13427472531
step 14: 26954944962
+ 26944945962
step 15: 53899890924
+ 42909899835
step 16: 96809790759
+ 95709790869
step 17: 192519581628
+ 826185915291
step 18: 1018705496919
+ 9196945078101
step 19: 10215650575020
+ 02057505651201
step 20: 12273156226221
+ 12262265137221
step 21: 24535421363442
+ 24436312453542
step 22: 48971733816984
+ 48961833717984
step 23: 97933567534968
+ 86943576533979
step 24: 184877144068947
+ 749860441778481
step 25: 934737585847428
+ 824748585737439
step 26: 1759486171584867
+ 7684851716849571
step 27: 9444337888434438
+ 8344348887334449
step 28: 17788686775768887
+ 78886757768688771
step 29: 96675444544457658
+ 85675444544457669
step 30: 182350889088915327
+ 723519880988053281
step 31: 905870770076968608
+ 806869670077078509
step 32: 1712740440154047117
+ 7117404510440472171
step 33: 8830144950594519288
+ 8829154950594410388
step 34: 17659299901188929676
+ 67692988110999295671
step 35: 85352288012188225347
+ 74352288121088225358
step 36: 159704576133276450705
+ 507054672331675407951
step 37: 666759248464951858656
+ 656858159464842957666
step 38: 1323617407929794816322
+ 2236184979297047163231
step 39: 3559802387226841979553
+ 3559791486227832089553
step 40: 7119593873454674069106
+ 6019604764543783959117
step 41: 13139198637998458028223
+ 32282085489973689193131
step 42: 45421284127972147221354
+ 45312274127972148212454
step 43: 90733558255944295433808
+ 80833459244955285533709
step 44: 171567017500899580967517
+ 715769085998005710765171
step 45: 887336103498905291732688
+ 886237192509894301633788
step 46: 1773573296008799593366476
+ 6746633959978006923753771
step 47: 8520207255986806517120247
+ 7420217156086895527020258
step 48: 15940424412073702044140505
+ 50504144020737021442404951
step 49: 66444568432810723486545456
+ 65454568432701823486544466
step 50: 131899136865512546973089922
+ 229980379645215568631998131
step 51: 361879516510728115605088053
+ 350880506511827015615978163
step 52: 712760023022555131221066216
+ 612660122131555220320067217
step 53: 1325420145154110351541133433
+ 3343311451530114515410245231
step 54: 4668731596684224866951378664
10833 takes 54 iterations / steps to resolve into a 28 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 1,716,984 times since Saturday, March 9th, 2002.)