Find the pattern of the following sequence and determine the next few terms:
2, 10, 12, 38, 42, 52, 56, 142, 150, 170
(In reply to
re(2): Official solution by Hugo)
Nikki's right -- the sequence is determined by those numbers for which the reverse of the ones complement is equal to the original number. The inverse of the reverse of the ones complement will be the original number for any palindromic binary number - 5, 21, or 51 as you suggested.
My solution could have added a column to make things more clear, I suppose, although in the table of valid values it is the same as the first. Notice that the selected rows are the only ones for which the first and third columns are equal:
Value Binary 1sComp Reverse
1 1 0 0
2 10 01 10 ***
3 11 00 00
4 100 011 110
5 101 010 010
6 110 001 100
7 111 000 000
8 1000 0111 1110
9 1001 0110 0110
10 1010 0101 1010 ***
11 1011 0100 0010
12 1100 0011 1100 ***
13 1101 0010 0100
14 1110 0001 1000
15 1111 0000 0000
16 10000 01111 11110
17 10001 01110 01110
18 10010 01101 10110
19 10011 01100 00110
20 10100 01011 11010
21 10101 01010 01010
22 10110 01001 10010
23 10111 01000 00010
24 11000 00111 11100
25 11001 00110 01100
26 11010 00101 10100
27 11011 00100 00100
28 11100 00011 11000
29 11101 00010 01000
30 11110 00001 10000
31 11111 00000 00000
32 100000 011111 111110
33 100001 011110 011110
34 100010 011101 101110
35 100011 011100 001110
36 100100 011011 110110
37 100101 011010 010110
38 100110 011001 100110 ***
39 100111 011000 000110
40 101000 010111 111010
41 101001 010110 011010
42 101010 010101 101010 ***
43 101011 010100 001010
44 101100 010011 110010
45 101101 010010 010010
46 101110 010001 100010
47 101111 010000 000010
48 110000 001111 111100
49 110001 001110 011100
50 110010 001101 101100
51 110011 001100 001100
52 110100 001011 110100 ***
53 110101 001010 010100
54 110110 001001 100100
55 110111 001000 000100
56 111000 000111 111000 ***
57 111001 000110 011000
58 111010 000101 101000
59 111011 000100 001000
60 111100 000011 110000
61 111101 000010 010000
62 111110 000001 100000
63 111111 000000 000000
64 1000000 0111111 1111110
65 1000001 0111110 0111110
66 1000010 0111101 1011110
67 1000011 0111100 0011110
68 1000100 0111011 1101110
69 1000101 0111010 0101110
70 1000110 0111001 1001110
71 1000111 0111000 0001110
72 1001000 0110111 1110110
73 1001001 0110110 0110110
74 1001010 0110101 1010110
75 1001011 0110100 0010110
76 1001100 0110011 1100110
77 1001101 0110010 0100110
78 1001110 0110001 1000110
79 1001111 0110000 0000110
80 1010000 0101111 1111010
81 1010001 0101110 0111010
82 1010010 0101101 1011010
83 1010011 0101100 0011010
84 1010100 0101011 1101010
85 1010101 0101010 0101010
86 1010110 0101001 1001010
87 1010111 0101000 0001010
88 1011000 0100111 1110010
89 1011001 0100110 0110010
90 1011010 0100101 1010010
91 1011011 0100100 0010010
92 1011100 0100011 1100010
93 1011101 0100010 0100010
94 1011110 0100001 1000010
95 1011111 0100000 0000010
96 1100000 0011111 1111100
97 1100001 0011110 0111100
98 1100010 0011101 1011100
99 1100011 0011100 0011100
100 1100100 0011011 1101100
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Posted by DJ
on 2004-12-18 08:36:21 |
re: Official solution
