A213204 Number of terms of the Collatz (3x+1) trajectory of n that are greater than or equal to n.

1, 1, 6, 1, 3, 4, 13, 1, 14, 2, 9, 2, 4, 9, 12, 1, 5, 8, 11, 1, 3, 5, 8, 1, 11, 2, 103, 4, 6, 9, 98, 1, 11, 3, 6, 3, 5, 6, 18, 1, 98, 2, 11, 2, 4, 6, 93, 1, 6, 5, 8, 1, 3, 96, 99, 1, 10, 2, 12, 5, 7, 92, 94, 1, 6, 4, 7, 1, 3, 4, 88, 1, 98, 2, 8, 2, 4, 11, 14

Offset

1,3

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A222597(n) - 1.

Example

For n=3, the Collatz trajectory is 3, 10, 5, 16, 8, 4, 2, 1 and hence a(3)=6.

Maple

b:= proc(n, m) option remember; `if`(n>=m, 1, 0)+
     `if`(n=1, 0, b(`if`(n::even, n/2, 3*n+1), m))
    end:
a:= n-> b(n$2):
seq(a(n), n=1..79);  # Alois P. Heinz, Dec 02 2025

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Select[Collatz[n], # >= n &]], {n, 100}]

Crossrefs

Cf. A076228, A222597.

Sequence in context: A273191 A086316 A021167 * A085677 A321093 A219552

Adjacent sequences: A213201 A213202 A213203 * A213205 A213206 A213207

Keyword

nonn

Author

Jayanta Basu, Mar 01 2013

Status

approved