A274467 Numbers that are the largest value in the Collatz (3x+1) trajectories of exactly six initial values.

16, 232, 340, 448, 1204, 1636, 1960, 2176, 2500, 2608, 3256, 3472, 3688, 3796, 3904, 4336, 4552, 4768, 5092, 5200, 5416, 5632, 5956, 6064, 6496, 6928, 7252, 7360, 7576, 8116, 8548, 8656, 8872, 8980, 9304, 9412, 9520, 9736, 9952, 10168, 10384, 10600, 10708, 10816, 11032, 11464, 11572, 11680

Offset: 1

Author

Hartmut F. W. Hoft, Jun 24 2016

Keywords

• nonn

Comments

Numbers that appear exactly 6 times in A025586, which gives the largest value in the 3x + 1 trajectory of n. This sequence is a subsequence of A033496 and also of A176869.

There is a single Collatz trajectory containing all initial values to its maximum value n which has the form (8n-20)/9, (4n-10)/9, (2n-5)/9, (2n-2)/3, (n-1)/3, n, where n mod 3 = 1, (2n-2)/3 mod 3 = 1, (4n-10)/9 mod 3 = 0; see also the link in A033496.

Examples

			1636 is in the sequence since it is the largest value in the single trajectory starting with 1452, 726, 363, 1090, 545, 1636, and no other initial values produce a trajectory with maximum 1636.
		

Links

• Hartmut F. W. Hoft, Table of n, a(n) for n = 1..5320

Crossrefs

Cf. A025586, A033496, A176869, A232870.

Programs

Mathematica

(* function fanSize[] is defined in A105730 *)
a274467[low_, high_] := First[Transpose[Select[Map[{#, fanSize[#]}&, Range[low, high, 4]], Last[#]==6&]]]/; Mod[low, 4]==0
a274467[4,10000] (* Data *)