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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A025586, A033496, A176869, A232870.

Sequence in context: A028340 A166903 A230234 * A119463 A292341 A222389

Adjacent sequences: A274464 A274465 A274466 * A274468 A274469 A274470

Keyword

nonn

Author

Hartmut F. W. Hoft, Jun 24 2016

Status

approved