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

1,2

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.

Links

Table of n, a(n) for n=1..46.

Example

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

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

Crossrefs

Cf. A301937, A304030.

Sequence in context: A294476 A258087 A191130 * A310165 A310166 A310167

Adjacent sequences: A319735 A319736 A319737 * A319739 A319740 A319741

Keyword

nonn

Author

Robert G. Wilson v, Sep 26 2018

Status

approved