REVERSAL-ADDITION PALINDROME TEST ON 150296

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 150296:
150296
+ 692051
step 1: 842347
+ 743248
step 2: 1585595
+ 5955851
step 3: 7541446
+ 6441457
step 4: 13982903
+ 30928931
step 5: 44911834
+ 43811944
step 6: 88723778
+ 87732788
step 7: 176456566
+ 665654671
step 8: 842111237
+ 732111248
step 9: 1574222485
+ 5842224751
step 10: 7416447236
+ 6327446147
step 11: 13743893383
+ 38339834731
step 12: 52083728114
+ 41182738025
step 13: 93266466139
+ 93166466239
step 14: 186432932378
+ 873239234681
step 15: 1059672167059
+ 9507612769501
step 16: 10567284936560
+ 06563948276501
step 17: 17131233213061
+ 16031233213171
step 18: 33162466426232
+ 23262466426133
step 19: 56424932852365
+ 56325823942465
step 20: 112750756794830
+ 038497657057211
step 21: 151248413852041
+ 140258314842151
step 22: 291506728694192
+ 291496827605192
step 23: 583003556299384
+ 483992655300385
step 24: 1066996211599769
+ 9679951126996601
step 25: 10746947338596370
+ 07369583374964701
step 26: 18116530713561071
+ 17016531703561181
step 27: 35133062417122252
+ 25222171426033153
step 28: 60355233843155405
+ 50455134833255306
step 29: 110810368676410711
+ 117014676863018011
step 30: 227825045539428722
+ 227824935540528722
step 31: 455649981079957444
+ 444759970189946554
step 32: 900409951269903998
+ 899309962159904009
step 33: 1799719913429808007
+ 7008089243199179971
step 34: 8807809156628987978
+ 8797898266519087088
step 35: 17605707423148075066
+ 66057084132470750671
step 36: 83662791555618825737
+ 73752881655519726638
step 37: 157415673211138552375
+ 573255831112376514751
step 38: 730671504323515067126
+ 621760515323405176037
step 39: 1352432019646920243163
+ 3613420296469102342531
step 40: 4965852316116022585694
+ 4965852206116132585694
step 41: 9931704522232155171388
+ 8831715512322254071399
step 42: 18763420034554409242787
+ 78724290445543002436781
step 43: 97487710480097411679568
+ 86597611479008401778479
step 44: 184085321959105813458047
+ 740854318501959123580481
step 45: 924939640461064937038528
+ 825830739460164046939429
step 46: 1750770379921228983977957
+ 7597793898221299730770571
step 47: 9348564278142528714748528
+ 8258474178252418724658439
step 48: 17607038456394947439406967
+ 76960493474949365483070671
step 49: 94567531931344312922477638
+ 83677422921344313913576549
step 50: 178244954852688626836054187
+ 781450638626886258459442871
step 51: 959695593479574885295497058
+ 850794592588475974395596959
step 52: 1810490186068050859691094017
+ 7104901969580508606810940181
step 53: 8915392155648559466502034198
+ 8914302056649558465512935198
step 54: 17829694212298117932014969396
+ 69396941023971189221249692871
step 55: 87226635236269307153264662267
+ 76226646235170396263253662278
step 56: 163453281471439703416518324545
+ 545423815614307934174182354361
step 57: 708877097085747637590700678906
+ 609876007095736747580790778807
step 58: 1318753104181484385171491457713
+ 3177541941715834841814013578131
step 59: 4496295045897319226985505035844
+ 4485305055896229137985405926944
step 60: 8981600101793548364970910962788
+ 8872690190794638453971010061898
step 61: 17854290292588186818941921024686
+ 68642012914981868188529209245871
step 62: 86496303207570055007471130270557
+ 75507203117470055007570230369468
step 63: 162003506325040110015041360640025
+ 520046063140510011040523605300261
step 64: 682049569465550121055564965940286
150296 takes 64 iterations / steps to resolve into a 33 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 1,717,002 times since Saturday, March 9th, 2002.)