[ExI] taxi numbers

Tue Jan 24 05:09:01 UTC 2023

Thx Giovanni,

Do allow me to propose some terminology.  Any number which can be expressed as the sum of two cubes two or more different ways is a taxicab number.

Any taxicab number which can be expressed as sum of cubes exactly 2 ways is a 2 taxi or double taxi as you suggested.  All of those on your list below are double taxis.

Any number which can be expressed as the sum of cubes exactly three ways is a triple taxi and so on.

I found 8 triple taxis yesterday and will see if I can find about the same number in the next half hour.  Hint: I discovered a marvelous algorithm, not the one posted earlier.  I think I shall call it… hmmm… something creative, such as... spike’s taxi algorithm.

spike

From: extropy-chat <extropy-chat-bounces at lists.extropy.org> On Behalf Of Giovanni Santostasi via extropy-chat
Sent: Monday, 23 January, 2023 7:59 PM
To: ExI chat list <extropy-chat at lists.extropy.org>
Cc: Giovanni Santostasi <gsantostasi at gmail.com>
Subject: Re: [ExI] taxi numbers

Spike,

Here the 2 Taxi numbers up to 10^7. I made also a map of the components (first number bigger in green and second number red). Not sure it means anything but there is an interesting gap in the middle. I will try the 3 Taxi numbers overnight. In the following list the first number is the taxi number, the following 2 are the cubes of the first sum and the 2 following numbers are the cubes of the second sum. 

1729 12 1 9 10
4104 16 2 9 15
13832 24 2 18 20
20683 27 10 19 24
32832 32 4 18 30
39312 34 2 15 33
40033 34 9 16 33
46683 36 3 27 30
64232 39 17 26 36
65728 40 12 31 33
110656 48 4 36 40
110808 48 6 27 45
134379 51 12 38 43
149389 53 8 29 50
165464 54 20 38 48
171288 55 17 24 54
195841 58 9 22 57
216027 60 3 22 59
216125 60 5 45 50
262656 64 8 36 60
314496 68 4 30 66
320264 68 18 32 66
327763 67 30 51 58
373464 72 6 54 60
402597 69 42 56 61
439101 76 5 48 69
443889 76 17 38 73
513000 80 10 45 75
513856 78 34 52 72
515375 80 15 54 71
525824 80 24 62 66
558441 81 30 57 72
593047 84 7 63 70
684019 82 51 64 75
704977 89 2 41 86
805688 93 11 30 92
842751 94 23 63 84
885248 96 8 72 80
886464 96 12 54 90
920673 97 20 33 96
955016 98 24 63 89
984067 98 35 59 92
994688 99 29 60 92
1009736 96 50 59 93
1016496 97 47 66 90
1061424 102 6 45 99
1073375 102 23 60 95
1075032 102 24 76 86
1080891 102 27 48 99
1092728 103 1 64 94
1195112 106 16 58 100
1260441 108 9 81 90
1323712 108 40 76 96
1331064 110 4 67 101
1370304 110 34 48 108
1407672 112 14 63 105
1533357 109 62 90 93
1566728 116 18 44 114
1609272 113 55 92 94
1728216 120 6 44 118
1729000 120 10 90 100
1734264 117 51 78 108
1774656 120 36 93 99
1845649 121 42 49 120
2048391 127 2 95 106
2101248 128 16 72 120
2301299 132 11 99 110
2418271 134 23 95 116
2515968 136 8 60 132
2562112 136 36 64 132
2585375 135 50 95 120
2622104 134 60 102 116
2691451 139 18 94 123
2864288 142 10 103 121
2987712 144 12 108 120
2991816 144 18 81 135
3220776 138 84 112 122
3242197 141 76 85 138
3375001 150 1 73 144
3375008 150 2 83 141
3511872 152 4 41 151
3512808 152 10 96 138
3551112 152 34 76 146
3587409 153 18 121 122
3628233 153 36 114 129
3798613 156 13 117 130
3813992 156 26 123 125
4033503 159 24 87 150
4104000 160 20 90 150
4110848 156 68 104 144
4123000 160 30 108 142
4174281 161 10 84 153
4206592 160 48 124 132
4342914 163 23 121 137
4467528 162 60 114 144
4505949 165 24 86 157
4511808 165 27 100 152
4607064 166 32 129 135
4624776 165 51 72 162
4673088 167 25 64 164
4744376 168 14 126 140
4914000 170 10 75 165
4931101 165 76 102 157
5004125 170 45 80 165
5135104 172 36 93 163
5287707 174 27 66 171
5318677 174 37 136 141
5446359 172 71 135 144
5462424 176 22 99 165
5472152 164 102 128 150
5639816 178 4 82 172
5772403 178 51 115 162
5799339 179 40 107 166
5832729 180 9 66 177
5835375 180 15 135 150
6013000 178 72 115 165
6017193 180 57 113 166
6058747 172 99 120 163
6230504 184 10 67 181
6434883 186 3 59 184
6445504 186 22 60 184
6517000 184 66 105 175
6742008 188 46 126 168
7081984 192 16 144 160
7091712 192 24 108 180
7094269 189 70 133 168
7365384 194 40 66 192
7620661 196 45 133 174
7640128 196 48 126 178
7872536 196 70 118 184
7882245 192 93 149 166
7957504 198 58 120 184
8029000 195 85 130 180
8077888 192 100 118 186
8131968 194 94 132 180
8216000 200 60 155 165
8275176 202 32 129 183
8491392 204 12 90 198
8493039 204 15 79 200
8494577 204 17 153 170
8587000 204 46 120 190
8600256 204 48 152 172
8647128 204 54 96 198
8741824 206 2 128 188
8849601 201 90 153 174
8872487 207 14 140 183
9016488 208 26 117 195
9261729 210 9 161 172
9443761 209 68 146 185
9560896 212 32 116 200

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