The sequence 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, . . . is formed from all positive integers that are either a power of 2 or a sum of two distinct powers of 2. Find the 200th term of this sequence.
clc, clearvars
a=2.^[0:40];
b=[0 a];
[p,q] = meshgrid(a, b);
pairs = [p(:) q(:)];
s=[];
for i=1:length(pairs)
if pairs(i,1)~=pairs(i,2)
s(end+1)= pairs(i,1)+pairs(i,2);
end
end
s=unique(s);
for i=1:220
fprintf('%3d %8d\n',i,s(i))
end
The 200th element in the list of the first 220, shown below, is 524,544.
In binary it's 10000000000100000000 so it's 2^19+2^8.
1 1
2 2
3 3
4 4
5 5
6 6
7 8
8 9
9 10
10 12
11 16
12 17
13 18
14 20
15 24
16 32
17 33
18 34
19 36
20 40
21 48
22 64
23 65
24 66
25 68
26 72
27 80
28 96
29 128
30 129
31 130
32 132
33 136
34 144
35 160
36 192
37 256
38 257
39 258
40 260
41 264
42 272
43 288
44 320
45 384
46 512
47 513
48 514
49 516
50 520
51 528
52 544
53 576
54 640
55 768
56 1024
57 1025
58 1026
59 1028
60 1032
61 1040
62 1056
63 1088
64 1152
65 1280
66 1536
67 2048
68 2049
69 2050
70 2052
71 2056
72 2064
73 2080
74 2112
75 2176
76 2304
77 2560
78 3072
79 4096
80 4097
81 4098
82 4100
83 4104
84 4112
85 4128
86 4160
87 4224
88 4352
89 4608
90 5120
91 6144
92 8192
93 8193
94 8194
95 8196
96 8200
97 8208
98 8224
99 8256
100 8320
101 8448
102 8704
103 9216
104 10240
105 12288
106 16384
107 16385
108 16386
109 16388
110 16392
111 16400
112 16416
113 16448
114 16512
115 16640
116 16896
117 17408
118 18432
119 20480
120 24576
121 32768
122 32769
123 32770
124 32772
125 32776
126 32784
127 32800
128 32832
129 32896
130 33024
131 33280
132 33792
133 34816
134 36864
135 40960
136 49152
137 65536
138 65537
139 65538
140 65540
141 65544
142 65552
143 65568
144 65600
145 65664
146 65792
147 66048
148 66560
149 67584
150 69632
151 73728
152 81920
153 98304
154 131072
155 131073
156 131074
157 131076
158 131080
159 131088
160 131104
161 131136
162 131200
163 131328
164 131584
165 132096
166 133120
167 135168
168 139264
169 147456
170 163840
171 196608
172 262144
173 262145
174 262146
175 262148
176 262152
177 262160
178 262176
179 262208
180 262272
181 262400
182 262656
183 263168
184 264192
185 266240
186 270336
187 278528
188 294912
189 327680
190 393216
191 524288
192 524289
193 524290
194 524292
195 524296
196 524304
197 524320
198 524352
199 524416
200 524544
201 524800
202 525312
203 526336
204 528384
205 532480
206 540672
207 557056
208 589824
209 655360
210 786432
211 1048576
212 1048577
213 1048578
214 1048580
215 1048584
216 1048592
217 1048608
218 1048640
219 1048704
220 1048832
|
|
Posted by Charlie
on 2025-03-03 13:18:13 |
computer solution
