REVERSAL-ADDITION PALINDROME TEST ON 600589

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 600589:
600589
+ 985006
step 1: 1585595
+ 5955851
step 2: 7541446
+ 6441457
step 3: 13982903
+ 30928931
step 4: 44911834
+ 43811944
step 5: 88723778
+ 87732788
step 6: 176456566
+ 665654671
step 7: 842111237
+ 732111248
step 8: 1574222485
+ 5842224751
step 9: 7416447236
+ 6327446147
step 10: 13743893383
+ 38339834731
step 11: 52083728114
+ 41182738025
step 12: 93266466139
+ 93166466239
step 13: 186432932378
+ 873239234681
step 14: 1059672167059
+ 9507612769501
step 15: 10567284936560
+ 06563948276501
step 16: 17131233213061
+ 16031233213171
step 17: 33162466426232
+ 23262466426133
step 18: 56424932852365
+ 56325823942465
step 19: 112750756794830
+ 038497657057211
step 20: 151248413852041
+ 140258314842151
step 21: 291506728694192
+ 291496827605192
step 22: 583003556299384
+ 483992655300385
step 23: 1066996211599769
+ 9679951126996601
step 24: 10746947338596370
+ 07369583374964701
step 25: 18116530713561071
+ 17016531703561181
step 26: 35133062417122252
+ 25222171426033153
step 27: 60355233843155405
+ 50455134833255306
step 28: 110810368676410711
+ 117014676863018011
step 29: 227825045539428722
+ 227824935540528722
step 30: 455649981079957444
+ 444759970189946554
step 31: 900409951269903998
+ 899309962159904009
step 32: 1799719913429808007
+ 7008089243199179971
step 33: 8807809156628987978
+ 8797898266519087088
step 34: 17605707423148075066
+ 66057084132470750671
step 35: 83662791555618825737
+ 73752881655519726638
step 36: 157415673211138552375
+ 573255831112376514751
step 37: 730671504323515067126
+ 621760515323405176037
step 38: 1352432019646920243163
+ 3613420296469102342531
step 39: 4965852316116022585694
+ 4965852206116132585694
step 40: 9931704522232155171388
+ 8831715512322254071399
step 41: 18763420034554409242787
+ 78724290445543002436781
step 42: 97487710480097411679568
+ 86597611479008401778479
step 43: 184085321959105813458047
+ 740854318501959123580481
step 44: 924939640461064937038528
+ 825830739460164046939429
step 45: 1750770379921228983977957
+ 7597793898221299730770571
step 46: 9348564278142528714748528
+ 8258474178252418724658439
step 47: 17607038456394947439406967
+ 76960493474949365483070671
step 48: 94567531931344312922477638
+ 83677422921344313913576549
step 49: 178244954852688626836054187
+ 781450638626886258459442871
step 50: 959695593479574885295497058
+ 850794592588475974395596959
step 51: 1810490186068050859691094017
+ 7104901969580508606810940181
step 52: 8915392155648559466502034198
+ 8914302056649558465512935198
step 53: 17829694212298117932014969396
+ 69396941023971189221249692871
step 54: 87226635236269307153264662267
+ 76226646235170396263253662278
step 55: 163453281471439703416518324545
+ 545423815614307934174182354361
step 56: 708877097085747637590700678906
+ 609876007095736747580790778807
step 57: 1318753104181484385171491457713
+ 3177541941715834841814013578131
step 58: 4496295045897319226985505035844
+ 4485305055896229137985405926944
step 59: 8981600101793548364970910962788
+ 8872690190794638453971010061898
step 60: 17854290292588186818941921024686
+ 68642012914981868188529209245871
step 61: 86496303207570055007471130270557
+ 75507203117470055007570230369468
step 62: 162003506325040110015041360640025
+ 520046063140510011040523605300261
step 63: 682049569465550121055564965940286
600589 takes 63 iterations / steps to resolve into a 33 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 1,768,546 times since Saturday, March 9th, 2002.)