A303876 a(n) is (apparently) the largest number k whose Collatz (or '3x+1') trajectory includes the number k + n.

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

Offset: 1

Author

Jon E. Schoenfield, May 01 2018

Keywords

• nonn

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.)

Examples

			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.
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A070993.