REVERSAL-ADDITION PALINDROME TEST ON 10069785

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 10069785:
10069785
+ 58796001
step 1: 68865786
+ 68756886
step 2: 137622672
+ 276226731
step 3: 413849403
+ 304948314
step 4: 718797717
+ 717797817
step 5: 1436595534
+ 4355956341
step 6: 5792551875
+ 5781552975
step 7: 11574104850
+ 05840147511
step 8: 17414252361
+ 16325241471
step 9: 33739493832
+ 23839493733
step 10: 57578987565
+ 56578987575
step 11: 114157975140
+ 041579751411
step 12: 155737726551
+ 155627737551
step 13: 311365464102
+ 201464563113
step 14: 512830027215
+ 512720038215
step 15: 1025550065430
+ 0345600555201
step 16: 1371150620631
+ 1360260511731
step 17: 2731411132362
+ 2632311141372
step 18: 5363722273734
+ 4373722273635
step 19: 9737444547369
+ 9637454447379
step 20: 19374898994748
+ 84749989847391
step 21: 104124888842139
+ 931248888421401
step 22: 1035373777263540
+ 0453627773735301
step 23: 1489001550998841
+ 1488990551009841
step 24: 2977992102008682
+ 2868002012997792
step 25: 5845994115006474
+ 4746005114995485
step 26: 10591999230001959
+ 95910003299919501
step 27: 106502002529921460
+ 064129925200205601
step 28: 170631927730127061
+ 160721037729136071
step 29: 331352965459263132
+ 231362954569253133
step 30: 562715920028516265
+ 562615820029517265
step 31: 1125331740058033530
+ 0353308500471335211
step 32: 1478640240529368741
+ 1478639250420468741
step 33: 2957279490949837482
+ 2847389490949727592
step 34: 5804668981899565074
+ 4705659981898664085
step 35: 10510328963798229159
+ 95192289736982301501
step 36: 105702618700780530660
+ 066035087007816207501
step 37: 171737705708596738161
+ 161837695807507737171
step 38: 333575401516104475332
+ 233574401615104575333
step 39: 567149803131209050665
+ 566050902131308941765
step 40: 1133200705262517992430
+ 0342997152625070023311
step 41: 1476197857887588015741
+ 1475108857887587916741
step 42: 2951306715775175932482
+ 2842395715775176031592
step 43: 5793702431550351964074
+ 4704691530551342073975
step 44: 10498393962101694038049
+ 94083049610126939389401
step 45: 104581443572228633427450
+ 054724336822275344185401
step 46: 159305780394503977612851
+ 158216779305493087503951
step 47: 317522559699997065116802
+ 208611560799996955225713
step 48: 526134120499994020342515
+ 515243020499994021431625
step 49: 1041377140999988041774140
+ 0414771408899990417731401
step 50: 1456148549899978459505541
+ 1455059548799989458416541
step 51: 2911208098699967917922082
+ 2802297197699968908021192
step 52: 5713505296399936825943274
+ 4723495286399936925053175
step 53: 10437000582799873750996449
+ 94469905737899728500073401
step 54: 104906906320699602251069850
+ 058960152206996023609609401
step 55: 163867058527695625860679251
+ 152976068526596725850768361
step 56: 316843127054292351711447612
+ 216744117153292450721348613
step 57: 533587244207584802432796225
+ 522697234208485702442785335
step 58: 1056284478416070504875581560
+ 0651855784050706148744826501
step 59: 1708140262466776653620408061
+ 1608040263566776642620418071
step 60: 3316180526033553296240826132
+ 2316280426923553306250816133
step 61: 5632460952957106602491642265
+ 5622461942066017592590642365
step 62: 11254922895023124195082284630
+ 03648228059142132059822945211
step 63: 14903150954165256254905229841
+ 14892250945265256145905130941
step 64: 29795401899430512400810360782
+ 28706301800421503499810459792
step 65: 58501703699852015900620820574
+ 47502802600951025899630710585
step 66: 106004506300803041800251531159
+ 951135152008140308003605400601
step 67: 1057139658308943349803856931760
+ 0671396583089433498038569317501
step 68: 1728536241398376847842426249261
+ 1629426242487486738931426358271
step 69: 3357962483885863586773852607532
+ 2357062583776853685883842697533
step 70: 5715025067662717272657695305065
+ 5605035967562727172667605205175
step 71: 11320061035225444445325300510240
+ 04201500352354444452253016002311
step 72: 15521561387579888897578316512551
10069785 takes 72 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 1,792,389 times since Saturday, March 9th, 2002.)