REVERSAL-ADDITION PALINDROME TEST ON 1998999

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 1998999:
1998999
+ 9998991
step 1: 11997990
+ 09979911
step 2: 21977901
+ 10977912
step 3: 32955813
+ 31855923
step 4: 64811736
+ 63711846
step 5: 128523582
+ 285325821
step 6: 413849403
+ 304948314
step 7: 718797717
+ 717797817
step 8: 1436595534
+ 4355956341
step 9: 5792551875
+ 5781552975
step 10: 11574104850
+ 05840147511
step 11: 17414252361
+ 16325241471
step 12: 33739493832
+ 23839493733
step 13: 57578987565
+ 56578987575
step 14: 114157975140
+ 041579751411
step 15: 155737726551
+ 155627737551
step 16: 311365464102
+ 201464563113
step 17: 512830027215
+ 512720038215
step 18: 1025550065430
+ 0345600555201
step 19: 1371150620631
+ 1360260511731
step 20: 2731411132362
+ 2632311141372
step 21: 5363722273734
+ 4373722273635
step 22: 9737444547369
+ 9637454447379
step 23: 19374898994748
+ 84749989847391
step 24: 104124888842139
+ 931248888421401
step 25: 1035373777263540
+ 0453627773735301
step 26: 1489001550998841
+ 1488990551009841
step 27: 2977992102008682
+ 2868002012997792
step 28: 5845994115006474
+ 4746005114995485
step 29: 10591999230001959
+ 95910003299919501
step 30: 106502002529921460
+ 064129925200205601
step 31: 170631927730127061
+ 160721037729136071
step 32: 331352965459263132
+ 231362954569253133
step 33: 562715920028516265
+ 562615820029517265
step 34: 1125331740058033530
+ 0353308500471335211
step 35: 1478640240529368741
+ 1478639250420468741
step 36: 2957279490949837482
+ 2847389490949727592
step 37: 5804668981899565074
+ 4705659981898664085
step 38: 10510328963798229159
+ 95192289736982301501
step 39: 105702618700780530660
+ 066035087007816207501
step 40: 171737705708596738161
+ 161837695807507737171
step 41: 333575401516104475332
+ 233574401615104575333
step 42: 567149803131209050665
+ 566050902131308941765
step 43: 1133200705262517992430
+ 0342997152625070023311
step 44: 1476197857887588015741
+ 1475108857887587916741
step 45: 2951306715775175932482
+ 2842395715775176031592
step 46: 5793702431550351964074
+ 4704691530551342073975
step 47: 10498393962101694038049
+ 94083049610126939389401
step 48: 104581443572228633427450
+ 054724336822275344185401
step 49: 159305780394503977612851
+ 158216779305493087503951
step 50: 317522559699997065116802
+ 208611560799996955225713
step 51: 526134120499994020342515
+ 515243020499994021431625
step 52: 1041377140999988041774140
+ 0414771408899990417731401
step 53: 1456148549899978459505541
+ 1455059548799989458416541
step 54: 2911208098699967917922082
+ 2802297197699968908021192
step 55: 5713505296399936825943274
+ 4723495286399936925053175
step 56: 10437000582799873750996449
+ 94469905737899728500073401
step 57: 104906906320699602251069850
+ 058960152206996023609609401
step 58: 163867058527695625860679251
+ 152976068526596725850768361
step 59: 316843127054292351711447612
+ 216744117153292450721348613
step 60: 533587244207584802432796225
+ 522697234208485702442785335
step 61: 1056284478416070504875581560
+ 0651855784050706148744826501
step 62: 1708140262466776653620408061
+ 1608040263566776642620418071
step 63: 3316180526033553296240826132
+ 2316280426923553306250816133
step 64: 5632460952957106602491642265
+ 5622461942066017592590642365
step 65: 11254922895023124195082284630
+ 03648228059142132059822945211
step 66: 14903150954165256254905229841
+ 14892250945265256145905130941
step 67: 29795401899430512400810360782
+ 28706301800421503499810459792
step 68: 58501703699852015900620820574
+ 47502802600951025899630710585
step 69: 106004506300803041800251531159
+ 951135152008140308003605400601
step 70: 1057139658308943349803856931760
+ 0671396583089433498038569317501
step 71: 1728536241398376847842426249261
+ 1629426242487486738931426358271
step 72: 3357962483885863586773852607532
+ 2357062583776853685883842697533
step 73: 5715025067662717272657695305065
+ 5605035967562727172667605205175
step 74: 11320061035225444445325300510240
+ 04201500352354444452253016002311
step 75: 15521561387579888897578316512551
1998999 takes 75 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 1,749,618 times since Saturday, March 9th, 2002.)