# 山水娱乐

•  REVERSAL-ADDITION PALINDROME TEST ON 1009150

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 1009150:
 1009150 + 0519001 step 1: 1528151 + 1518251 step 2: 3046402 + 2046403 step 3: 5092805 + 5082905 step 4: 10175710 + 01757101 step 5: 11932811 + 11823911 step 6: 23756722 + 22765732 step 7: 46522454 + 45422564 step 8: 91945018 + 81054919 step 9: 172999937 + 739999271 step 10: 912999208 + 802999219 step 11: 1715998427 + 7248995171 step 12: 8964993598 + 8953994698 step 13: 17918988296 + 69288981971 step 14: 87207970267 + 76207970278 step 15: 163415940545 + 545049514361 step 16: 708465454906 + 609454564807 step 17: 1317920019713 + 3179100297131 step 18: 4497020316844 + 4486130207944 step 19: 8983150524788 + 8874250513898 step 20: 17857401038686 + 68683010475871 step 21: 86540411514557 + 75541511404568 step 22: 162081922919125 + 521919229180261 step 23: 684001152099386 + 683990251100486 step 24: 1367991403199872 + 2789913041997631 step 25: 4157904445197503 + 3057915444097514 step 26: 7215819889295017 + 7105929889185127 step 27: 14321749778480144 + 44108487794712341 step 28: 58430237573192485 + 58429137573203485 step 29: 116859375146395970 + 079593641573958611 step 30: 196453016720354581 + 185453027610354691 step 31: 381906044330709272 + 272907033440609183 step 32: 654813077771318455 + 554813177770318456 step 33: 1209626255541636911 + 1196361455526269021 step 34: 2405987711067905932 + 2395097601177895042 step 35: 4801085312245800974 + 4790085422135801084 step 36: 9591170734381602058 + 8502061834370711959 step 37: 18093232568752314017 + 71041325786523239081 step 38: 89134558355275553098 + 89035557255385543198 step 39: 178170115610661096296 + 692690166016511071871 step 40: 870860281627172168167 + 761861271726182068078 step 41: 1632721553353354236245 + 5426324533533551272361 step 42: 7059046086886905508606 + 6068055096886806409507 step 43: 13127101183773711918113 + 31181911737738110172131 step 44: 44309012921511822090244 + 44209022811512921090344 step 45: 88518035733024743180588 + 88508134742033753081588 step 46: 177026170475058496262176 + 671262694850574071620771 step 47: 848288865325632567882947 + 749288765236523568882848 step 48: 1597577630562156136765795 + 5975676316512650367757951 step 49: 7573253947074806504523746 + 6473254056084707493523757 step 50: 14046508003159513998047503 + 30574089931595130080564041 step 51: 44620597934754644078611544 + 44511687044645743979502644 step 52: 89132284979400388058114188 + 88141185088300497948223198 step 53: 177273470067700886006337386 + 683733600688007760074372771 step 54: 861007070755708646080710157 + 751017080646807557070700168 step 55: 1612024151402516203151410325 + 5230141513026152041514202161 step 56: 6842165664428668244665612486
1009150 takes 56 iterations / steps to resolve into a 28 digit palindrome.

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 2,061,766 times since Saturday, March 9th, 2002.)