REVERSAL-ADDITION PALINDROME TEST ON 7008429

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 7008429:
7008429
+ 9248007
step 1: 16256436
+ 63465261
step 2: 79721697
+ 79612797
step 3: 159334494
+ 494433951
step 4: 653768445
+ 544867356
step 5: 1198635801
+ 1085368911
step 6: 2284004712
+ 2174004822
step 7: 4458009534
+ 4359008544
step 8: 8817018078
+ 8708107188
step 9: 17525125266
+ 66252152571
step 10: 83777277837
+ 73877277738
step 11: 157654555575
+ 575555456751
step 12: 733210012326
+ 623210012337
step 13: 1356420024663
+ 3664200246531
step 14: 5020620271194
+ 4911720260205
step 15: 9932340531399
+ 9931350432399
step 16: 19863690963798
+ 89736909636891
step 17: 109600600600689
+ 986006006006901
step 18: 1095606606607590
+ 0957066066065901
step 19: 2052672672673491
+ 1943762762762502
step 20: 3996435435435993
+ 3995345345346993
step 21: 7991780780782986
+ 6892870870871997
step 22: 14884651651654983
+ 38945615615648841
step 23: 53830267267303824
+ 42830376276203835
step 24: 96660643543507659
+ 95670534534606669
step 25: 192331178078114328
+ 823411870871133291
step 26: 1015743048949247619
+ 9167429498403475101
step 27: 10183172547352722720
+ 02722725374527138101
step 28: 12905897921879860821
+ 12806897812979850921
step 29: 25712795734859711742
+ 24711795843759721752
step 30: 50424591578619433494
+ 49433491687519542405
step 31: 99858083266138975899
+ 99857983166238085899
step 32: 199716066432377061798
+ 897160773234660617991
step 33: 1096876839667037679789
+ 9879767307669386786901
step 34: 10976644147336424466690
+ 09666442463374144667901
step 35: 20643086610710569134591
+ 19543196501701668034602
step 36: 40186283112412237169193
+ 39196173221421138268104
step 37: 79382456333833375437297
+ 79273457333833365428397
step 38: 158655913667666740865694
+ 496568047666766319556851
step 39: 655223961334433060422545
+ 545224060334433169322556
step 40: 1200448021668866229745101
+ 1015479226688661208440021
step 41: 2215927248357527438185122
+ 2215818347257538427295122
step 42: 4431745595615065865480244
+ 4420845685605165955471344
step 43: 8852591281220231820951588
+ 8851590281320221821952588
step 44: 17704181562540453642904176
+ 67140924635404526518140771
step 45: 84845106197944980161044947
+ 74944016108944979160154848
step 46: 159789122306889959321199795
+ 597991123959988603221987951
step 47: 757780246266878562543187746
+ 647781345265878662642087757
step 48: 1405561591532757225185275503
+ 3055725815227572351951655041
step 49: 4461287406760329577136930544
+ 4450396317759230676047821644
step 50: 8911683724519560253184752188
+ 8812574813520659154273861198
step 51: 17724258538040219407458613386
+ 68331685470491204083585242771
step 52: 86055944008531423491043856157
+ 75165834019432413580044955068
step 53: 161221778027963837071088811225
+ 522118880170738369720877122161
step 54: 683340658198702206791965933386
+ 683339569197602207891856043386
step 55: 1366680227396304414683821976772
+ 2776791283864144036937220866631
step 56: 4143471511260448451621042843403
+ 3043482401261548440621151743414
step 57: 7186953912521996892242194586817
+ 7186854912422986991252193596817
step 58: 14373808824944983883494388183634
+ 43638188349438838944942880837341
step 59: 58011997174383822828437269020975
+ 57902096273482822838347179911085
step 60: 115914093447866645666784448932060
+ 060239844487666546668744390419511
step 61: 176153937935533192335528839351571
+ 175153938825533291335539739351671
step 62: 351307876761066483671068578703242
+ 242307875860176384660167678703153
step 63: 593615752621242868331236257406395
+ 593604752632133868242126257516395
step 64: 1187220505253376736573362514922790
+ 0972294152633756376733525050227811
step 65: 2159514657887133113306887565150601
+ 1060515657886033113317887564159512
step 66: 3220030315773166226624775129310113
+ 3110139215774266226613775130300223
step 67: 6330169531547432453238550259610336
+ 6330169520558323542347451359610336
step 68: 12660339052105755995586001619220672
+ 27602291610068559955750125093306621
step 69: 40262630662174315951336126712527293
+ 39272521762163315951347126603626204
step 70: 79535152424337631902683253316153497
+ 79435161335238620913673342425153597
step 71: 158970313759576252816356595741307094
+ 490703147595653618252675957313079851
step 72: 649673461355229871069032553054386945
+ 549683450355230960178922553164376946
step 73: 1199356911710460831247955106218763891
+ 1983678126015597421380640171196539911
step 74: 3183035037726058252628595277415303802
+ 2083035147725958262528506277305303813
step 75: 5266070185452016515157101554720607615
+ 5167060274551017515156102545810706625
step 76: 10433130460003034030313204100531314240
+ 04241313500140231303043030006403133401
step 77: 14674443960143265333356234106934447641
7008429 takes 77 iterations / steps to resolve into a 38 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 1,792,530 times since Saturday, March 9th, 2002.)