REVERSAL-ADDITION PALINDROME TEST ON 1008628

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 1008628:
1008628
+ 8268001
step 1: 9276629
+ 9266729
step 2: 18543358
+ 85334581
step 3: 103877939
+ 939778301
step 4: 1043656240
+ 0426563401
step 5: 1470219641
+ 1469120741
step 6: 2939340382
+ 2830439392
step 7: 5769779774
+ 4779779675
step 8: 10549559449
+ 94495594501
step 9: 105045153950
+ 059351540501
step 10: 164396694451
+ 154496693461
step 11: 318893387912
+ 219783398813
step 12: 538676786725
+ 527687676835
step 13: 1066364463560
+ 0653644636601
step 14: 1720009100161
+ 1610019000271
step 15: 3330028100432
+ 2340018200333
step 16: 5670046300765
+ 5670036400765
step 17: 11340082701530
+ 03510728004311
step 18: 14850810705841
+ 14850701805841
step 19: 29701512511682
+ 28611521510792
step 20: 58313034022474
+ 47422043031385
step 21: 105735077053859
+ 958350770537501
step 22: 1064085847591360
+ 0631957485804601
step 23: 1696043333395961
+ 1695933333406961
step 24: 3391976666802922
+ 2292086666791933
step 25: 5684063333594855
+ 5584953333604865
step 26: 11269016667199720
+ 02799176661096211
step 27: 14068193328295931
+ 13959282339186041
step 28: 28027475667481972
+ 27918476657472082
step 29: 55945952324954054
+ 45045942325954955
step 30: 100991894650909009
+ 900909056498199001
step 31: 1001900951149108010
+ 0108019411590091001
step 32: 1109920362739199011
+ 1109919372630299011
step 33: 2219839735369498022
+ 2208949635379389122
step 34: 4428789370748887144
+ 4417888470739878244
step 35: 8846677841488765388
+ 8835678841487766488
step 36: 17682356682976531876
+ 67813567928665328671
step 37: 85495924611641860547
+ 74506814611642959458
step 38: 160002739223284820005
+ 500028482322937200061
step 39: 660031221546222020066
+ 660020222645122130066
step 40: 1320051444191344150132
+ 2310514431914441500231
step 41: 3630565876105785650363
+ 3630565875016785650363
step 42: 7261131751122571300726
+ 6270031752211571311627
step 43: 13531163503334142612353
+ 35321624143330536113531
step 44: 48852787646664678725884
1008628 takes 44 iterations / steps to resolve into a 23 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 1,768,459 times since Saturday, March 9th, 2002.)