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A303876 a(n) is (apparently) the largest number k whose Collatz (or '3x+1') trajectory includes the number k + n. 0
7287, 7286, 9229, 9228, 9227, 9226, 6147, 9224, 2299, 9222, 9221, 9220, 4255, 3335, 4843, 4086, 7271, 4598, 4839, 3057, 5003, 1758, 7265, 6130, 8511, 8510, 6671, 6670, 7259, 4586, 6667, 7023, 11347, 11346, 15039, 15131, 14695, 8892, 13447, 6114, 10007, 10006 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Terms listed in the Data section are from an exhaustive search through k = 10^8. (The search for a(1) was performed up through k = 10^9; see A070993.)
It seems extremely unlikely that any larger value of k begins a trajectory that includes k+1. (Note that none of the terms listed in the Data exceed 15131.)
LINKS
EXAMPLE
a(1) = 7287 is apparently the last term of A070993 ("Numbers n such that the trajectory of n under the '3x+1' map reaches n+1"); the trajectory of k = 7287 begins with 7287, 21862, 10931, 32794, 16397, 49192, 24596, 12298, 6149, 18448, 9224, 4612, 2306, 1153, 3460, 1730, 865, 2596, 1298, 649, 1948, 974, 487, 1462, 731, 2194, 1097, 3292, 1646, 823, 2470, 1235, 3706, 1853, 5560, 2780, 1390, 695, 2086, 1043, 3130, 1565, 4696, 2348, 1174, 587, 1762, 881, 2644, 1322, 661, 1984, 992, 496, 248, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, ..., reaching 7288 = k+1 at the 120th term of the trajectory.
CROSSREFS
Sequence in context: A152502 A251226 A260000 * A358855 A031799 A250638
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, May 01 2018
STATUS
approved

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Last modified July 12 12:19 EDT 2024. Contains 374247 sequences. (Running on oeis4.)