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A355312
Irregular triangle read by rows, in which the rows list groups of consecutive integers taking the same number of halving and tripling steps to reach 1 in '3X+1' problem. Groups are in order of the number of steps required, and in numerical order among those with the same number of steps.
1
20, 21, 12, 13, 84, 85, 52, 53, 340, 341, 34, 35, 212, 213, 226, 227, 1364, 1365, 68, 69, 70, 452, 453, 454, 22, 23, 140, 141, 150, 151, 852, 853, 908, 909, 5460, 5461, 44, 45, 46, 276, 277, 300, 301, 302, 1812, 1813, 14, 15, 92, 93, 564, 565, 604, 605, 3412, 3413
OFFSET
1,1
EXAMPLE
20 and 21 are terms since they both use 7 steps (trajectories 20, 10, 5, 16, 8, 4, 2, 1 and 21, 64, 32, 16, 8, 4, 2, 1).
300, 301 and 302 are terms since they all use 16 steps.
The triangle starts:
7: 20 21
9: 12 13 84 85
11: 52 53 340 341
13: 34 35 212 213 226 227 1364 1365
14: 68 69 70 452 453 454
15: 22 23 140 141 150 151 852 853 908 909 5460 5461
16: 44 45 46 276 277 300 301 302 1812 1813
17: 14 15 92 93 564 565 604 605 3412 3413
PROG
(PARI) See Links section.
CROSSREFS
Subtriangle of A127824.
Sequence in context: A165841 A222958 A374170 * A212284 A091235 A078286
KEYWORD
nonn,tabf
AUTHOR
Paul Duckett, Jun 27 2022
STATUS
approved