REVERSAL-ADDITION PALINDROME TEST ON 1008595

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 1008595:
1008595
+ 5958001
step 1: 6966596
+ 6956696
step 2: 13923292
+ 29232931
step 3: 43156223
+ 32265134
step 4: 75421357
+ 75312457
step 5: 150733814
+ 418337051
step 6: 569070865
+ 568070965
step 7: 1137141830
+ 0381417311
step 8: 1518559141
+ 1419558151
step 9: 2938117292
+ 2927118392
step 10: 5865235684
+ 4865325685
step 11: 10730561369
+ 96316503701
step 12: 107047065070
+ 070560740701
step 13: 177607805771
+ 177508706771
step 14: 355116512542
+ 245215611553
step 15: 600332124095
+ 590421233006
step 16: 1190753357101
+ 1017533570911
step 17: 2208286928012
+ 2108296828022
step 18: 4316583756034
+ 4306573856134
step 19: 8623157612168
+ 8612167513268
step 20: 17235325125436
+ 63452152353271
step 21: 80687477478707
+ 70787477478608
step 22: 151474954957315
+ 513759459474151
step 23: 665234414431466
+ 664134414432566
step 24: 1329368828864032
+ 2304688288639231
step 25: 3634057117503263
+ 3623057117504363
step 26: 7257114235007626
+ 6267005324117527
step 27: 13524119559125153
+ 35152195591142531
step 28: 48676315150267684
+ 48676205151367684
step 29: 97352520301635368
+ 86353610302525379
step 30: 183706130604160747
+ 747061406031607381
step 31: 930767536635768128
+ 821867536635767039
step 32: 1752635073271535167
+ 7615351723705362571
step 33: 9367986796976897738
+ 8377986796976897639
step 34: 17745973593953795377
+ 77359735939537954771
step 35: 95105709533491750148
+ 84105719433590750159
step 36: 179211428967082500307
+ 703005280769824112971
step 37: 882216709736906613278
+ 872316609637907612288
step 38: 1754533319374814225566
+ 6655224184739133354571
step 39: 8409757504113947580137
+ 7310857493114057579048
step 40: 15720614997228005159185
+ 58195150082279941602751
step 41: 73915765079507946761936
+ 63916764970597056751937
step 42: 137832530050105003513873
+ 378315300501050035238731
step 43: 516147830551155038752604
+ 406257830551155038741615
step 44: 922405661102310077494219
+ 912494770013201166504229
step 45: 1834900431115511243998448
+ 8448993421155111340094381
step 46: 10283893852270622584092829
+ 92829048522607225839838201
step 47: 103112942374877848423931030
+ 030139324848778473249211301
step 48: 133252267223656321673142331
+ 133241376123656322762252331
step 49: 266493643347312644435394662
+ 266493534446213743346394662
step 50: 532987177793526387781789324
+ 423987187783625397771789235
step 51: 956974365577151785553578559
+ 955875355587151775563479659
step 52: 1912849721164303561117058218
+ 8128507111653034611279482191
step 53: 10041356832817338172396540409
+ 90404569327183371823865314001
step 54: 100445926160000709996261854410
+ 014458162699907000061629544001
step 55: 114904088859907710057891398411
+ 114893198750017709958880409411
step 56: 229797287609925420016771807822
+ 228708177610024529906782797922
step 57: 458505465219949949923554605744
+ 447506455329949949912564505854
step 58: 906011920549899899836119111598
+ 895111911638998998945029110609
step 59: 1801123832188898898781148222207
+ 7022228411878988988812383211081
step 60: 8823352244067887887593531433288
+ 8823341353957887887604422533288
step 61: 17646693598025775775197953966576
+ 67566935979157757752089539664671
step 62: 85213629577183533527287493631247
+ 74213639478272533538177592631258
step 63: 159427269055456067065465086262505
+ 505262680564560760654550962724951
step 64: 664689949620016827720016048987456
+ 654789840610027728610026949986466
step 65: 1319479790230044556330042998973922
+ 2293798992400336554400320979749131
step 66: 3613278782630381110730363978723053
+ 3503278793630370111830362878723163
step 67: 7116557576260751222560726857446216
+ 6126447586270652221570626757556117
step 68: 13243005162531403444131353615002333
+ 33320051635313144430413526150034231
step 69: 46563056797844547874544879765036564
1008595 takes 69 iterations / steps to resolve into a 35 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 2,542,395 times since Saturday, March 9th, 2002.)