REVERSAL-ADDITION PALINDROME TEST ON 1000689

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 1000689:
1000689
+ 9860001
step 1: 10860690
+ 09606801
step 2: 20467491
+ 19476402
step 3: 39943893
+ 39834993
step 4: 79778886
+ 68887797
step 5: 148666683
+ 386666841
step 6: 535333524
+ 425333535
step 7: 960667059
+ 950766069
step 8: 1911433128
+ 8213341191
step 9: 10124774319
+ 91347742101
step 10: 101472516420
+ 024615274101
step 11: 126087790521
+ 125097780621
step 12: 251185571142
+ 241175581152
step 13: 492361152294
+ 492251163294
step 14: 984612315588
+ 885513216489
step 15: 1870125532077
+ 7702355210781
step 16: 9572480742858
+ 8582470842759
step 17: 18154951585617
+ 71658515945181
step 18: 89813467530798
+ 89703576431898
step 19: 179517043962696
+ 696269340715971
step 20: 875786384678667
+ 766876483687578
step 21: 1642662868366245
+ 5426638682662461
step 22: 7069301551028706
+ 6078201551039607
step 23: 13147503102068313
+ 31386020130574131
step 24: 44533523232642444
+ 44424623232533544
step 25: 88958146465175988
+ 88957156464185988
step 26: 177915302929361976
+ 679163929203519771
step 27: 857079232132881747
+ 747188231232970758
step 28: 1604267463365852505
+ 5052585633647624061
step 29: 6656853097013476566
+ 6656743107903586566
step 30: 13313596204917063132
+ 23136071940269531331
step 31: 36449668145186594463
+ 36449568154186694463
step 32: 72899236299373288926
+ 62988237399263299827
step 33: 135887473698636588753
+ 357885636896374788531
step 34: 493773110595011377284
+ 482773110595011377394
step 35: 976546221190022754678
+ 876457220091122645679
step 36: 1853003441281145400357
+ 7530045411821443003581
step 37: 9383048853102588403938
+ 8393048852013588403839
step 38: 17776097705116176807777
+ 77770867161150779067771
step 39: 95546964866266955875548
+ 84557855966266846964559
step 40: 180104820832533802840107
+ 701048208335238028401081
step 41: 881153029167771831241188
+ 881142138177761920351188
step 42: 1762295167345533751592376
+ 6732951573355437615922671
step 43: 8495246740700971367515047
+ 7405157631790070476425948
step 44: 15900404372491041843940995
+ 59904934814019427340400951
step 45: 75805339186510469184341946
+ 64914348196401568193350857
step 46: 140719687382912037377692803
+ 308296773730219283786917041
step 47: 449016461113131321164609844
+ 448906461123131311164610944
step 48: 897922922236262632329220788
+ 887022923236262632229229798
step 49: 1784945845472525264558450586
+ 6850548554625252745485494871
step 50: 8635494400097778010043945457
+ 7545493400108777900044945368
step 51: 16180987800206555910088890825
+ 52809888001955560200878908161
step 52: 68990875802162116110967798986
+ 68989776901161126120857809986
step 53: 137980652703323242231825608972
+ 279806528132242323307256089731
step 54: 417787180835565565539081698703
+ 307896180935565565538081787714
step 55: 725683361771131131077163486417
+ 714684361770131131177163386527
step 56: 1440367723541262262254326872944
+ 4492786234522622621453277630441
step 57: 5933153958063884883707604503385
+ 5833054067073884883608593513395
step 58: 11766208025137769767316198016780
+ 08761089161376796773152080266711
step 59: 20527297186514566540468278283491
+ 19438287286404566541568179272502
step 60: 39965584472919133082036457555993
+ 39955575463028033191927448556993
step 61: 79921159935947166273963906112986
+ 68921160936937266174953995112997
step 62: 148842320872884432448917901225983
+ 389522109719844234488278023248841
step 63: 538364430592728666937195924474824
+ 428474429591739666827295034463835
step 64: 966838860184468333764490958938659
+ 956839859094467333864481068838669
step 65: 1923678719278935667628972027777328
+ 8237777202798267665398729178763291
step 66: 10161455922077203333027701206540619
+ 91604560210772033330277022955416101
step 67: 101766016132849236663304724161956720
+ 027659161427403366632948231610667101
step 68: 129425177560252603296252955772623821
+ 128326277559252692306252065771524921
step 69: 257751455119505295602505021544148742
+ 247841445120505206592505911554157752
step 70: 505592900240010502195010933098306494
+ 494603890339010591205010042009295505
step 71: 1000196790579021093400020975107601999
+ 9991067015790200043901209750976910001
step 72: 10991263806369221137301230726084512000
+ 00021548062703210373112296360836219901
step 73: 11012811869072431510413527086920731901
+ 10913702968072531401513427096811821011
step 74: 21926514837144962911926954183732552912
+ 21925523738145962911926944173841562912
step 75: 43852038575290925823853898357574115824
+ 42851147575389835832852909257583025834
step 76: 86703186150680761656706807615157141658
+ 85614175151670860765616708605168130768
step 77: 172317361302351622422323516220325272426
+ 624272523022615323224226153203163713271
step 78: 796589884324966945646549669423488985697
1000689 takes 78 iterations / steps to resolve into a 39 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 1,717,008 times since Saturday, March 9th, 2002.)