There is something odd about the number 153. if you start calculating with it, 153 is found in every 3rd number, as i proof in below table for the first 150 numbers. Also note that every last result before the final one always is either 351 or 513.
BaseNumber = (1 * 3) = 3
(33)=27
27 = 27
New number = 27
(23)=8
(73)=343
8 + 343 = 351
New number = 351
(53)=125
(13)=1
27 + 125 + 1 = 153
number of steps to 153 = 3
BaseNumber = (2 * 3) = 6
(63)=216
216 = 216
New number = 216
8 + 1 + 216 = 225
New number = 225
8 + 8 + 125 = 141
New number = 141
(43)=64
1 + 64 + 1 = 66
New number = 66
216 + 216 = 432
New number = 432
64 + 27 + 8 = 99
New number = 99
(93)=729
729 + 729 = 1458
New number = 1458
(83)=512
1 + 64 + 125 + 512 = 702
New number = 702
(03)=0
343 + 0 + 8 = 351
number of steps to 153 = 10
BaseNumber = (3 * 3) = 9
729 = 729
New number = 729
343 + 8 + 729 = 1080
New number = 1080
1 + 0 + 512 + 0 = 513
New number = 513
125 + 1 + 27 = 153
number of steps to 153 = 4
BaseNumber = (4 * 3) = 12
1 + 8 = 9
New number = 9
number of steps to 153 = 5
BaseNumber = (5 * 3) = 15
1 + 125 = 126
New number = 126
1 + 8 + 216 = 225
BaseNumber = (6 * 3) = 18
1 + 512 = 513
number of steps to 153 = 2
BaseNumber = (7 * 3) = 21
8 + 1 = 9
BaseNumber = (8 * 3) = 24
8 + 64 = 72
New number = 72
343 + 8 = 351
BaseNumber = (9 * 3) = 27
BaseNumber = (10 * 3) = 30
27 + 0 = 27
BaseNumber = (11 * 3) = 33
27 + 27 = 54
New number = 54
125 + 64 = 189
New number = 189
1 + 512 + 729 = 1242
New number = 1242
1 + 8 + 64 + 8 = 81
New number = 81
512 + 1 = 513
number of steps to 153 = 6
BaseNumber = (12 * 3) = 36
27 + 216 = 243
New number = 243
8 + 64 + 27 = 99
BaseNumber = (13 * 3) = 39
27 + 729 = 756
New number = 756
343 + 125 + 216 = 684
New number = 684
216 + 512 + 64 = 792
New number = 792
343 + 729 + 8 = 1080
BaseNumber = (14 * 3) = 42
64 + 8 = 72
BaseNumber = (15 * 3) = 45
64 + 125 = 189
BaseNumber = (16 * 3) = 48
64 + 512 = 576
New number = 576
125 + 343 + 216 = 684
BaseNumber = (17 * 3) = 51
125 + 1 = 126
BaseNumber = (18 * 3) = 54
BaseNumber = (19 * 3) = 57
125 + 343 = 468
New number = 468
64 + 216 + 512 = 792
BaseNumber = (20 * 3) = 60
216 + 0 = 216
BaseNumber = (21 * 3) = 63
216 + 27 = 243
BaseNumber = (22 * 3) = 66
BaseNumber = (23 * 3) = 69
216 + 729 = 945
New number = 945
729 + 64 + 125 = 918
New number = 918
729 + 1 + 512 = 1242
BaseNumber = (24 * 3) = 72
BaseNumber = (25 * 3) = 75
343 + 125 = 468
BaseNumber = (26 * 3) = 78
343 + 512 = 855
New number = 855
512 + 125 + 125 = 762
New number = 762
343 + 216 + 8 = 567
New number = 567
125 + 216 + 343 = 684
number of steps to 153 = 8
BaseNumber = (27 * 3) = 81
BaseNumber = (28 * 3) = 84
512 + 64 = 576
BaseNumber = (29 * 3) = 87
512 + 343 = 855
BaseNumber = (30 * 3) = 90
729 + 0 = 729
BaseNumber = (31 * 3) = 93
729 + 27 = 756
BaseNumber = (32 * 3) = 96
729 + 216 = 945
BaseNumber = (33 * 3) = 99
BaseNumber = (34 * 3) = 102
1 + 0 + 8 = 9
BaseNumber = (35 * 3) = 105
1 + 0 + 125 = 126
BaseNumber = (36 * 3) = 108
1 + 0 + 512 = 513
BaseNumber = (37 * 3) = 111
1 + 1 + 1 = 3
New number = 3
BaseNumber = (38 * 3) = 114
1 + 1 + 64 = 66
number of steps to 153 = 7
BaseNumber = (39 * 3) = 117
1 + 1 + 343 = 345
New number = 345
27 + 64 + 125 = 216
number of steps to 153 = 11
BaseNumber = (40 * 3) = 120
1 + 8 + 0 = 9
BaseNumber = (41 * 3) = 123
1 + 8 + 27 = 36
New number = 36
BaseNumber = (42 * 3) = 126
number of steps to 153 = 9
BaseNumber = (43 * 3) = 129
1 + 8 + 729 = 738
New number = 738
343 + 27 + 512 = 882
New number = 882
512 + 512 + 8 = 1032
New number = 1032
1 + 0 + 27 + 8 = 36
BaseNumber = (44 * 3) = 132
1 + 27 + 8 = 36
BaseNumber = (45 * 3) = 135
1 + 27 + 125 = 153
number of steps to 153 = 1
BaseNumber = (46 * 3) = 138
1 + 27 + 512 = 540
New number = 540
125 + 64 + 0 = 189
BaseNumber = (47 * 3) = 141
BaseNumber = (48 * 3) = 144
1 + 64 + 64 = 129
New number = 129
BaseNumber = (49 * 3) = 147
1 + 64 + 343 = 408
New number = 408
64 + 0 + 512 = 576
BaseNumber = (50 * 3) = 150
1 + 125 + 0 = 126
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