Determine the smallest positive integer value of N such that 2022*N is a palindrome.
What is the next smallest positive integer value of N that satisfies the given conditions?
The short answer is 1101, and the next smallest is 2257.
The program gets the first ten:
clearvars,clc
n=2022; ct=0;mult=1;
while ct<10
n=n+2022; mult=mult+1;
ns=char(string(n));
good=true;
for i=1:floor(length(ns)/2)
if ns(i)~=ns(length(ns)+1-i)
good=false;
break
end
end
if good
disp([ n mult])
ct=ct+1;
end
end
finds the smallest 10:
the palindrome multiple of 2022
2226222 1101
4563654 2257
6789876 3358
6911196 3418
24488442 12111
25711752 12716
49088094 24277
62344326 30833
201474102 99641
213717312 105696
========================================
I figured, Why stop with 2022. Here are a few more years. Years ending in zero will never find a palindrome as the zero that's always at the end will keep getting removed from the beginning. Years ending in 5 sometimes have that problem, as in 2025.
2022
2226222 1101
4563654 2257
6789876 3358
6911196 3418
24488442 12111
25711752 12716
49088094 24277
62344326 30833
201474102 99641
213717312 105696
2023
801108 396
4365634 2158
5856585 2895
7321237 3619
8812188 4356
16400461 8107
64133146 31702
72522527 35849
80911908 39996
88922988 43956
2024
238832 118
487784 241
635536 314
884488 437
2151512 1063
4839384 2391
8029208 3967
8616168 4257
21177112 10463
21733712 10738
2025
2026
2465642 1217
2850582 1407
6353536 3136
62200226 30701
69888896 34496
81633618 40293
213767312 105512
217616712 107412
224373422 110747
228222822 112647
2027
1830381 903
2079702 1026
2708072 1336
5097905 2515
5726275 2825
8744478 4314
29788792 14696
33200233 16379
66400466 32758
76055067 37521
2028
2370732 1169
4457544 2198
6311136 3112
8681868 4281
40444404 19943
63399336 31262
69422496 34232
80888808 39886
86911968 42856
213252312 105154
2029
68986 34
1641461 809
3727273 1837
4191914 2066
6277726 3094
8870788 4372
9315139 4591
79522597 39193
84633648 41712
103010301 50769
2030
2031
1708071 841
10299201 5071
18788781 9251
29311392 14432
64922946 31966
85744758 42218
104131401 51271
113494311 55881
123060321 60591
200545002 98742
2032
2785872 1371
2958592 1456
6792976 3343
6965696 3428
61088016 30063
215424512 106016
217151712 106866
230888032 113626
236323632 116301
238050832 117151
2033
65056 32
9459549 4653
38933983 19151
77800877 38269
114797411 56467
143686341 70677
172575271 84887
221666122 109034
250555052 123244
285949582 140654
2034
648846 319
8190918 4027
8485848 4172
8943498 4397
83611638 41107
86855868 42702
200050002 98353
217979712 107168
219606912 107968
232787232 114448
2035
54945 27
531135 261
543345 267
555555 273
567765 279
579975 285
5280825 2595
5561655 2733
5695965 2799
5842485 2871
2036
425524 209
2996992 1472
4293924 2109
4823284 2369
6120216 3006
6507056 3196
42977924 21109
48800884 23969
61499416 30206
67322376 33066
2037
1350531 663
2823282 1386
5021205 2465
6371736 3128
7844487 3851
14855841 7293
16200261 7953
53888835 26455
55233255 27115
94266249 46277
2038
2188812 1074
4275724 2098
6362636 3122
8908098 4371
28000082 13739
41988914 20603
64944946 31867
69988996 34342
87900978 43131
207323702 101729
2039
1975791 969
2075702 1018
5923295 2905
6023206 2954
7998997 3923
8098908 3972
8771778 4302
31333313 15367
62666626 30734
66255266 32494
2040
2041
48984 24
3271723 1603
4457544 2184
8425248 4128
13044031 6391
22944922 11242
26088062 12782
35988953 17633
70877807 34727
79633697 39017
2042
8798978 4309
21922912 10736
42722724 20922
63522536 31108
69811896 34188
84322348 41294
203242302 99531
222151222 108791
241060142 118051
266707662 130611
2043
2439342 1194
2807082 1374
3985893 1951
6153516 3012
6521256 3192
12966921 6347
53822835 26345
67688676 33132
90633609 44363
102777201 50307
2044
42924 21
69496 34
292292 143
2520252 1233
2949492 1443
4069604 1991
6160616 3014
6589856 3224
8415148 4117
8680868 4247
2045
5245425 2565
5834385 2853
50366305 24629
56844865 27797
57699675 28215
501575105 245269
507464705 248149
515272515 251967
522303225 255405
523080325 255785
2046
87978 43
270072 132
2725272 1332
2970792 1452
20433402 9987
20944902 10237
22111122 10807
22622622 11057
24300342 11877
24811842 12127
2047
7248427 3541
8175718 3994
10200201 4983
20400402 9966
30600603 14949
40800804 19932
106818601 52183
112202211 54813
184686481 90223
190070091 92853
2048
405504 198
2977792 1454
4091904 1998
6547456 3197
8634368 4216
27011072 13189
40955904 19998
63911936 31207
67966976 33187
80222208 39171
2049
1288821 629
4089804 1996
6974796 3404
9775779 4771
26100162 12738
117282711 57239
121565121 59329
145292541 70909
178424871 87079
182707281 89169
2050
Edited on January 25, 2022, 1:34 pm
|
|
Posted by Charlie
on 2022-01-25 13:33:53 |
computer solution
