A319738 Numbers whose Collatz trajectories cross their initial values a record number of times.

1, 3, 6, 9, 14, 18, 33, 54, 97, 129, 194, 257, 294, 313, 342, 353, 398, 417, 470, 626, 9225, 13739, 14473, 19297, 27681, 38881, 112782, 283261, 427762, 506977, 831527, 876011, 1108702, 1168014, 1848673, 2191019, 5524041, 8546945, 10817230, 10964814, 11395926, 13506283, 15194569, 41698569, 46910891, 52774753

Offset: 1

Author

Robert G. Wilson v, Sep 26 2018

Keywords

• nonn

Comments

Indices at which records occur in A304030.

Number of crossings of a(n): 0, 1, 4, 5, 8, 10, 13, 14, 19, 27, 28, 29, 30, 31, 32, 37, 38, 45, 46, 50, 51, 55, 57, 59, 61, 69, 70, 71, 72, 77, 79, 81, 82, 88, 93, 97, 99, 113, 116, 120, 128, 129, 131, 139, 141, 143, ..., .

Also a(n) is a term of A301937.

Examples

			9 is a term since A304030(9) = 5 and 5 is greater than any previous term in A304030.
		

Crossrefs

Cf. A301937, A304030.

Programs

Mathematica

Collatz[n_] := NestWhileList[ If[ OddQ@#, 3# +1, #/2] &, n, # > 1 &]; f[n_] := Block[{x = Length[ SplitBy[ Collatz@n, # < n + 1 &]] - 1}, If[ OddQ@ n && n > 1, x - 1, x]]; mx = -1; k = 1; lst = {}; While[k < 5000001, If[ f@ k > mx, mx = f@ k; AppendTo[lst, k]]; k++]; lst