REVERSAL-ADDITION PALINDROME TEST ON 1001699

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 1001699:
1001699
+ 9961001
step 1: 10962700
+ 00726901
step 2: 11689601
+ 10698611
step 3: 22388212
+ 21288322
step 4: 43676534
+ 43567634
step 5: 87244168
+ 86144278
step 6: 173388446
+ 644883371
step 7: 818271817
+ 718172818
step 8: 1536444635
+ 5364446351
step 9: 6900890986
+ 6890980096
step 10: 13791871082
+ 28017819731
step 11: 41809690813
+ 31809690814
step 12: 73619381627
+ 72618391637
step 13: 146237773264
+ 462377732641
step 14: 608615505905
+ 509505516806
step 15: 1118121022711
+ 1172201218111
step 16: 2290322240822
+ 2280422230922
step 17: 4570744471744
+ 4471744470754
step 18: 9042488942498
+ 8942498842409
step 19: 17984987784907
+ 70948778948971
step 20: 88933766733878
+ 87833766733988
step 21: 176767533467866
+ 668764335767671
step 22: 845531869235537
+ 735532968135548
step 23: 1581064837371085
+ 5801737384601851
step 24: 7382802221972936
+ 6392791222082837
step 25: 13775593444055773
+ 37755044439557731
step 26: 51530637883613504
+ 40531638873603515
step 27: 92062276757217019
+ 91071275767226029
step 28: 183133552524443048
+ 840344425255331381
step 29: 1023477977779774429
+ 9244779777797743201
step 30: 10268257755577517630
+ 03671577555775286201
step 31: 13939835311352803831
+ 13830825311353893931
step 32: 27770660622706697762
+ 26779660722606607772
step 33: 54550321345313305534
+ 43550331354312305545
step 34: 98100652699625611079
+ 97011652699625600189
step 35: 195112305399251211268
+ 862112152993503211591
step 36: 1057224458392754422859
+ 9582244572938544227501
step 37: 10639469031331298650360
+ 06305689213313096493601
step 38: 16945158244644395143961
+ 16934159344644285154961
step 39: 33879317589288680298922
+ 22989208688298571397833
step 40: 56868526277587251696755
+ 55769615278577262586865
step 41: 112638141556164514283620
+ 026382415461655141836211
step 42: 139020557017819656119831
+ 138911656918710755020931
step 43: 277932213936530411140762
+ 267041114035639312239772
step 44: 544973327972169723380534
+ 435083327961279723379445
step 45: 980056655933449446759979
+ 979957644944339556650089
step 46: 1960014300877789003410068
+ 8600143009877780034100691
step 47: 10560157310755569037510759
+ 95701573096555701375106501
step 48: 106261730407311270412617260
+ 062716214072113704037162601
step 49: 168977944479424974449779861
1001699 takes 49 iterations / steps to resolve into a 27 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 1,750,282 times since Saturday, March 9th, 2002.)