REVERSAL-ADDITION PALINDROME TEST ON 1007619

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 1007619:
1007619
+ 9167001
step 1: 10174620
+ 02647101
step 2: 12821721
+ 12712821
step 3: 25534542
+ 24543552
step 4: 50078094
+ 49087005
step 5: 99165099
+ 99056199
step 6: 198221298
+ 892122891
step 7: 1090344189
+ 9814430901
step 8: 10904775090
+ 09057740901
step 9: 19962515991
+ 19951526991
step 10: 39914042982
+ 28924041993
step 11: 68838084975
+ 57948083886
step 12: 126786168861
+ 168861687621
step 13: 295647856482
+ 284658746592
step 14: 580306603074
+ 470306603085
step 15: 1050613206159
+ 9516023160501
step 16: 10566636366660
+ 06666363666501
step 17: 17233000033161
+ 16133000033271
step 18: 33366000066432
+ 23466000066333
step 19: 56832000132765
+ 56723100023865
step 20: 113555100156630
+ 036651001555311
step 21: 150206101711941
+ 149117101602051
step 22: 299323203313992
+ 299313302323992
step 23: 598636505637984
+ 489736505636895
step 24: 1088373011274879
+ 9784721103738801
step 25: 10873094115013680
+ 08631051149037801
step 26: 19504145264051481
+ 18415046254140591
step 27: 37919191518192072
+ 27029181519191973
step 28: 64948373037384045
+ 54048373037384946
step 29: 118996746074768991
+ 199867470647699811
step 30: 318864216722468802
+ 208864227612468813
step 31: 527728444334937615
+ 516739433444827725
step 32: 1044467877779765340
+ 0435679777787644401
step 33: 1480147655567409741
+ 1479047655567410841
step 34: 2959195311134820582
+ 2850284311135919592
step 35: 5809479622270740174
+ 4710470722269749085
step 36: 10519950344540489259
+ 95298404544305991501
step 37: 105818354888846480760
+ 067084648888453818501
step 38: 172903003777300299261
+ 162992003777300309271
step 39: 335895007554600608532
+ 235806006455700598533
step 40: 571701014010301207065
+ 560702103010410107175
step 41: 1132403117020711314240
+ 0424131170207113042311
step 42: 1556534287227824356551
1007619 takes 42 iterations / steps to resolve into a 22 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 2,549,842 times since Saturday, March 9th, 2002.)