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%I #6 May 03 2018 07:01:54
%S 7287,7286,9229,9228,9227,9226,6147,9224,2299,9222,9221,9220,4255,
%T 3335,4843,4086,7271,4598,4839,3057,5003,1758,7265,6130,8511,8510,
%U 6671,6670,7259,4586,6667,7023,11347,11346,15039,15131,14695,8892,13447,6114,10007,10006
%N a(n) is (apparently) the largest number k whose Collatz (or '3x+1') trajectory includes the number k + n.
%C 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.)
%C 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.)
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 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.
%Y Cf. A006370, A070993.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, May 01 2018
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