2497 * 1 = 2497
2497 * 2 = 4972
2497 * 3 = 7249
2497 * 4 = 9724
2497 * 5 = EEEE
186X35 * 1 = 186X35
186X35 * 2 = 35186X
186X35 * 3 = 5186X3
186X35 * 4 = 6X3518
186X35 * 5 = 86X351
186X35 * 6 = X35186
186X35 * 7 = EEEEEE
8579214E36429X7 * 1 = 8579214E36429X7
8579214E36429X7 * 2 = 14E36429X7085792
8579214E36429X7 * 3 = 214E36429X708579
8579214E36429X7 * 4 = 29X708579214E364
8579214E36429X7 * 5 = 36429X708579214E
8579214E36429X7 * 6 = 429X708579214E36
8579214E36429X7 * 7 = 4E36429X70857921
8579214E36429X7 * 8 = 579214E36429X708
8579214E36429X7 * 9 = 6429X708579214E3
8579214E36429X7 * X = 708579214E36429X
8579214E36429X7 * E = 79214E36429X7085
8579214E36429X7 * 10 = 8579214E36429X70
8579214E36429X7 * 11 = 9214E36429X70857
8579214E36429X7 * 12 = 9X708579214E3642
8579214E36429X7 * 13 = X708579214E36429
8579214E36429X7 * 14 = E36429X708579214
8579214E36429X7 * 15 = EEEEEEEEEEEEEEEE
123456789XE * 1 = 123456789XE
123456789XE * 2 = 2468E13579X
123456789XE * 3 = 36X147E2589
123456789XE * 4 = 4915X26E378
123456789XE * 5 = 5E4X3928167
123456789XE * 6 = 718293X4E56
123456789XE * 7 = 83E72X61945
123456789XE * 8 = 962E851X734
123456789XE * 9 = X8641E97523
123456789XE * X = EX987654312
123456789XE * E = 111111111101
123456789E * 1 = 123456789E (miss digit X)
123456789E * 2 = 2468E1357X (miss digit 9)
123456789E * 3 = 36X147E259 (miss digit 8)
123456789E * 4 = 4915X26E38 (miss digit 7)
123456789E * 5 = 5E4X392817 (miss digit 6)
123456789E * 6 = 718293X4E6 (miss digit 5)
123456789E * 7 = 83E72X6195 (miss digit 4)
123456789E * 8 = 962E851X74 (miss digit 3)
123456789E * 9 = X8641E9753 (miss digit 2)
123456789E * X = EX98765432 (miss digit 1)
123456789E * E = 11111111111
275 * 5 = 1111
275 * X = 2222
275 * 13 = 3333
275 * 18 = 4444
275 * 21 = 5555
275 * 26 = 6666
275 * 2E = 7777
275 * 34 = 8888
275 * 39 = 9999
275 * 42 = XXXX
275 * 47 = EEEE
1X537 * 7 = 111111
1X537 * 12 = 222222
1X537 * 19 = 333333
1X537 * 24 = 444444
1X537 * 2E = 555555
1X537 * 36 = 666666
1X537 * 41 = 777777
1X537 * 48 = 888888
1X537 * 53 = 999999
1X537 * 5X = XXXXXX
1X537 * 65 = EEEEEE
123456789E * E = 11111111111
123456789E * 1X = 22222222222
123456789E * 29 = 33333333333
123456789E * 38 = 44444444444
123456789E * 47 = 55555555555
123456789E * 56 = 66666666666
123456789E * 65 = 77777777777
123456789E * 74 = 88888888888
123456789E * 83 = 99999999999
123456789E * 92 = XXXXXXXXXXX
123456789E * X1 = EEEEEEEEEEE
92X79E43715865 * 15 = 1111111111111111
92X79E43715865 * 2X = 2222222222222222
92X79E43715865 * 43 = 3333333333333333
92X79E43715865 * 58 = 4444444444444444
92X79E43715865 * 71 = 5555555555555555
92X79E43715865 * 86 = 6666666666666666
92X79E43715865 * 9E = 7777777777777777
92X79E43715865 * E4 = 8888888888888888
92X79E43715865 * 109 = 9999999999999999
92X79E43715865 * 122 = XXXXXXXXXXXXXXXX
92X79E43715865 * 137 = EEEEEEEEEEEEEEEE
8327 * 17 = 111111
8327 * 32 = 222222
8327 * 49 = 333333
8327 * 64 = 444444
8327 * 7E = 555555
8327 * 96 = 666666
8327 * E1 = 777777
8327 * 108 = 888888
8327 * 123 = 999999
8327 * 13X = XXXXXX
8327 * 155 = EEEEEE
55 * 25 = 1111
55 * 4X = 2222
55 * 73 = 3333
55 * 98 = 4444
55 * 101 = 5555
55 * 126 = 6666
55 * 14E = 7777
55 * 174 = 8888
55 * 199 = 9999
55 * 202 = XXXX
55 * 227 = EEEE
1221 * E1 = 111111
1221 * 1X2 = 222222
1221 * 293 = 333333
1221 * 384 = 444444
1221 * 475 = 555555
1221 * 566 = 666666
1221 * 657 = 777777
1221 * 748 = 888888
1221 * 839 = 999999
1221 * 92X = XXXXXX
1221 * X1E = EEEEEE
112233445566778899XE * EE = 1111111111111111111111
112233445566778899XE * 1EX = 2222222222222222222222
112233445566778899XE * 2E9 = 3333333333333333333333
112233445566778899XE * 3E8 = 4444444444444444444444
112233445566778899XE * 4E7 = 5555555555555555555555
112233445566778899XE * 5E6 = 6666666666666666666666
112233445566778899XE * 6E5 = 7777777777777777777777
112233445566778899XE * 7E4 = 8888888888888888888888
112233445566778899XE * 8E3 = 9999999999999999999999
112233445566778899XE * 9E2 = XXXXXXXXXXXXXXXXXXXXXX
112233445566778899XE * XE1 = EEEEEEEEEEEEEEEEEEEEEE
E1X2938475665748392X1E1 * 121 = 11111111111111111111111111
E1X2938475665748392X1E1 * 242 = 22222222222222222222222222
E1X2938475665748392X1E1 * 363 = 33333333333333333333333333
E1X2938475665748392X1E1 * 484 = 44444444444444444444444444
E1X2938475665748392X1E1 * 5X5 = 55555555555555555555555555
E1X2938475665748392X1E1 * 706 = 66666666666666666666666666
E1X2938475665748392X1E1 * 827 = 77777777777777777777777777
E1X2938475665748392X1E1 * 948 = 88888888888888888888888888
E1X2938475665748392X1E1 * X69 = 99999999999999999999999999
E1X2938475665748392X1E1 * E8X = XXXXXXXXXXXXXXXXXXXXXXXXXX
E1X2938475665748392X1E1 * 10XE = EEEEEEEEEEEEEEEEEEEEEEEEEE
1^2 = 01, 0 + 1 = 1
E^2 = X1, X + 1 = E
56^2 = 2630, 26 + 30 = 56
66^2 = 3630, 36 + 30 = 66
EE^2 = EX01, EX + 01 = EE
444^2 = 170294, 170 + 294 = 444
778^2 = 4X4294, 4X4 + 294 = 778
EEE^2 = EEX001, EEX + 001 = EEE
12XX^2 = 1661144, 166 + 1144 = 12XX
1640^2 = 2401400, 240 + 1400 = 1640
2046^2 = 4161830, 416 + 1830 = 2046
2929^2 = 7802169, 780 + 2169 = 2929
3333^2 = X862469, X86 + 2469 = 3333
4973^2 = 1E062X69, 1E06 + 2X69 = 4973
5E60^2 = 2E603000, 2E60 + 3000 = 5E60
2^2 + 5^2 = 25
X^2 + 5^2 = X5
5^3 + 7^3 + 7^3 = 577
6^3 + 6^3 + 8^3 = 668
X^3 + 8^3 + 3^3 = X83
1^3 + 1^3 + X^3 + X^3 = 11XX
1^5 + 4^5 + 7^5 + 6^5 + 5^5 = 14765
9^5 + 3^5 + 8^5 + X^5 + 4^5 = 938X4
3^6 + 6^6 + 9^6 + 8^6 + 6^6 + 2^6 = 369862
X^6 + 2^6 + 3^6 + 9^6 + 4^6 + X^6 = X2394X
(X + 1)^2 = X1
(1 + 3 + 2 + 3)^3.6 = 1323
(3 + 9 + 6 + 9)^2.8 = 3969
(5 + 4 + 3 + 9)^3 = 5439
(6 + 1 + E + 4)^3 = 61E4
(7 + 0 + 5 + E)^3 = 705E
(1 + 6 + E + 6 + 8)^3 = 16E68
(1 + 8 + 9 + 6 + 9)^3 = 18969
(1 + X + 8 + E + 4)^3 = 1X8E4
(3 + 9 + 2 + 6 + 5)^3.6 = 39265
(1 + 1 + 5 + E + 4 + 1)^4 = 115E41
(4 + 9 + 2 + 3 + 6 + 9)^4 = 492369
X^1 + E^2 = XE
5^1 + 5^2 + 9^3 + 8^4 + 1^5 + 0^6 + 0^7 + 2^8 + E^9 = 55981002E
3^3 + X^X + 6^6 + 7^7 + X^X + 5^5 + 4^4 + 8^8 + 3^3 + 2^2 = 3X67X54832
3^3 + 2^9 + 1^0 = 390
55 * 99 = 4499
77 * 88 = 5588
XX * XX = 9944
66 * EE = 6556
14 = (1 * 4)^2
20 = (2^2 + 0^2)!
21 = (2^2 + 1^2)^2
24 = 2^2 + 4!
30 = ((3 + 0)!)^2
43 = 4! + 3^3
48 = 4^3 - 8
84 = (8 + sqrt(4))^2
X1 = (X + 1)^2
X5 = (X - 5)^3
X8 = (X - 8)^7
XE = X + E^2
121 = (12 - 1)^2
127 = 7 * 21
135 = 5 * 31
144 = 4 * 41
160 = (1 * 6 + 0)^3
163 = 3 * 61
169 = (1 * (6 + 9))^2
183 = ((1 + 8) / 3)^5
194 = ((1 - 9) / 4)^8
230 = (30 / 2)^2
243 = - 2^2 + (4 + 3)^3
247 = (2 - sqrt(4) + 7)^3
294 = (2 * 9 + sqrt(4))^2
344 = (3! + 4 * 4)^2
346 = 3^4 * 6
381 = (3 * 8 - 1)^2
441 = (4 + 1)^4
445 = 5^4 + 4
1 * X + 1 = E
12 * X + 2 = EX
123 * X + 3 = EX9
1234 * X + 4 = EX98
12345 * X + 5 = EX987
123456 * X + 6 = EX9876
1234567 * X + 7 = EX98765
12345678 * X + 8 = EX987654
123456789 * X + 9 = EX9876543
123456789X * X + X = EX98765432
123456789XE * X + E = EX987654321
123456789E00 * X + 10 = EX9876543210
0 * E + 1 = 1
1 * E + 2 = 11
12 * E + 3 = 111
123 * E + 4 = 1111
1234 * E + 5 = 11111
12345 * E + 6 = 111111
123456 * E + 7 = 1111111
1234567 * E + 8 = 11111111
12345678 * E + 9 = 111111111
123456789 * E + X = 1111111111
123456789X * E + E = 11111111111
123456789XE * E + 10 = 111111111111
1^2 = 1
11^2 = 121
111^2 = 12321
1111^2 = 1234321
11111^2 = 123454321
111111^2 = 12345654321
1111111^2 = 1234567654321
11111111^2 = 123456787654321
111111111^2 = 12345678987654321
1111111111^2 = 123456789X987654321
11111111111^2 = 123456789XEX987654321
111111111111^2 = 123456789E00EX987654321 (note: Rn^2 is not palindromic number if n ≥ 10)
E^2 = X1
EE^2 = EX01
EEE^2 = EEX001
EEEE^2 = EEEX0001
EEEEE^2 = EEEEX00001
EEEEEE^2 = EEEEEX000001
EEEEEEE^2 = EEEEEEX0000001
EEEEEEEE^2 = EEEEEEEX00000001
EEEEEEEEE^2 = EEEEEEEEX000000001
EEEEEEEEEE^2 = EEEEEEEEEX0000000001
EEEEEEEEEEE^2 = EEEEEEEEEEX00000000001
EEEEEEEEEEEE^2 = EEEEEEEEEEEX000000000001
3 * 4 = 10
33 * 44 = 1210
333 * 444 = 123210
3333 * 4444 = 12343210
33333 * 44444 = 1234543210
333333 * 444444 = 123456543210
3333333 * 4444444 = 12345676543210
33333333 * 44444444 = 1234567876543210
333333333 * 444444444 = 123456789876543210
3333333333 * 4444444444 = 123456789X9876543210
33333333333 * 44444444444 = 123456789XEX9876543210
333333333333 * 444444444444 = 123456789E00EX9876543210
6 * E = 56
66 * EE = 6556
666 * EEE = 665556
6666 * EEEE = 66655556
66666 * EEEEE = 6666555556
666666 * EEEEEE = 666665555556
6666666 * EEEEEEE = 66666655555556
66666666 * EEEEEEEE = 6666666555555556
666666666 * EEEEEEEEE = 666666665555555556
6666666666 * EEEEEEEEEE = 66666666655555555556
66666666666 * EEEEEEEEEEE = 6666666666555555555556
666666666666 * EEEEEEEEEEEE = 666666666665555555555556
10XE * 1 = 10XE
10XE * 2 = 219X
10XE * 3 = 3289
10XE * 4 = 4378
10XE * 5 = 5467
10XE * 6 = 6556
10XE * 7 = 7645
10XE * 8 = 8734
10XE * 9 = 9823
10XE * X = X912
10XE * E = EX01
10EXE * 1 = 10EXE
10EXE * 2 = 21E9X
10EXE * 3 = 32E89
10EXE * 4 = 43E78
10EXE * 5 = 54E67
10EXE * 6 = 65E56
10EXE * 7 = 76E45
10EXE * 8 = 87E34
10EXE * 9 = 98E23
10EXE * X = X9E12
10EXE * E = EXE01
1 / E = 0.111111111111 ...
1 / 11 = 0.0E 0E 0E 0E 0E 0E ...
1 / EE = 0.01 01 01 01 01 01 ...
1 / 101 = 0.00EE 00EE 00EE ...
1 / E1 = 0.010EXE 010EXE ...
1 / 111 = 0.00E 00E 00E 00E ...
1 / X1 = 0.0123456789E 0123456789E ...
1 / 121 = 0.00X28466482X0 EE1937557391E ...
1 / XE1 = 0.00112233445566778899XE 00112233445566778899XE ...
1 / XEE1 = 0.000111222333444555666777888999XXE 000111222333444555666777888999XXE ...
1 / XEEE1 = 0.0000111122223333444455556666777788889999XXXE 0000111122223333444455556666777788889999XXXE ...
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
1 / EEX001 = 0.000 001 002 003 004 005 006 007 008 009 00X 00E 010 011 012 013 014 ...
1 / EEEX0001 = 0.0000 0001 0002 0003 0004 0005 0006 0007 0008 0009 000X 000E 0010 0011 0012 0013 0014 ...
1 / EXE01 = 0.0000101111212222323333434444545555656666767777878888989999X9XXXXEE 0000101111212222323333434444545555656666767777878888989999X9XXXXEE ...
1 / EXEE = 0.00 01 01 02 03 05 08 11 19 2X 47 ...
1 / EEXEEE = 0.000 001 001 002 003 005 008 011 019 02X 047 075 100 175 275 42X 6X3 ...
1 / EEEXEEEE = 0.0000 0001 0001 0002 0003 0005 0008 0011 0019 002X 0047 0075 0100 0175 0275 042X 06X3 0E11 15E4 ...
1 / EX = 0.01 02 04 08 14 28 54 X8
194
368
714
1228
2454 ... (powers of 2)
1 / E9 = 0.01 03 09 23 69
183
509
1323
3969 ... (powers of 3)
1 / E8 = 0.01 04 14 54
194
714
2454 ... (powers of 4)
1 / XE = 0.0112358
11
19
2X
47
75
100
175
275
42X
6X3
E11
15E4 ... (Fibonacci numbers)
1 / 9E = 0.0125
10
25
5X
121
2X0
6X1
1462 ... (Pell numbers)
1 / 5E = 0.02 04 08 14 28 54 X8
194
368
714
1228
2454 ... (powers of 2)
1 / 3E = 0.03 09 23 69
183
509
1323
3969 ... (powers of 3)
1 / 2E = 0.04 14 54
194
714
2454 ... (powers of 4)
148421
28
54
X8
194
368
714
1228
1 / 1E = (powers of 2) ... 2454
23931
69
183
509
1323
1 / 2E = (power of 3) ... 3969
1441
54
194
714
1 / 3E = (power of 4) ... 2454
11853211
19
2X
47
75
100
175
275
42X
6X3
E11
1 / 10E = (Fibonacci numbers) ... 15E4
10521
25
5X
121
2X0
6X1
1 / 11E = (Pell numbers) ... 1462
ab * 5 * 25 = abab
ab * 7 * 17 * 111 = ababab
ab * 5 * 25 * 75 * 175 = abababab
ab * E0E1 * 11111 = ababababab
ab * 5 * 7 * 17 * 25 * 111 * EE01 = abababababab
abc * 7 * 11 * 17 = abcabc
abc * 31 * 3X891 = abcabcabc
abc * 5 * 7 * 11 * 17 * 25 * EE01 = abcabcabcabc
abcd * 75 * 175 = abcdabcd
abcd * 7 * 17 * 111 * EE01 = abcdabcdabcd
abcde * 11 * E0E1 = abcdeabcde
abcdef * 5 * 25 * EE01 = abcdefabcdef
(where a, b, c, d, e, f are any digits)
