A375280 Largest value in the trajectory of n in the A375265 map.

1, 2, 3, 4, 16, 6, 52, 8, 9, 16, 52, 12, 40, 52, 16, 16, 52, 18, 88, 20, 52, 52, 160, 24, 88, 40, 27, 52, 88, 30, 9232, 32, 52, 52, 160, 36, 112, 88, 40, 40, 9232, 52, 196, 52, 45, 160, 9232, 48, 148, 88, 52, 52, 160, 54, 9232, 56, 88, 88, 304, 60, 184, 9232, 63

Offset: 1

Author

Paolo Xausa, Aug 09 2024

Keywords

• nonn
• easy

Comments

By definition the trajectory ends when 1 is reached, so a(1) = 1.

Examples

			a(10) = 16 because 16 is the largest value in the trajectory 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem.

Crossrefs

Cf. A375265, A375266, A375267.

Cf. A025586, A365478.

Programs

Mathematica

A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[Max[NestWhileList[A375265, #, # > 1 &]] &, 100]

Formula

a(n) = max{A375266(n,k) for 1 <= k <= A375267(n) + 1}.