A222597 Number of terms of the Collatz (3x+1) trajectory of n that are greater than n.

0, 0, 5, 0, 2, 3, 12, 0, 13, 1, 8, 1, 3, 8, 11, 0, 4, 7, 10, 0, 2, 4, 7, 0, 10, 1, 102, 3, 5, 8, 97, 0, 10, 2, 5, 2, 4, 5, 17, 0, 97, 1, 10, 1, 3, 5, 92, 0, 5, 4, 7, 0, 2, 95, 98, 0, 9, 1, 11, 4, 6, 91, 93, 0, 5, 3, 6, 0, 2, 3, 87, 0, 97, 1, 7, 1, 3, 10, 13, 0, 6

Offset

1,3

Links

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

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..81);  # 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}]

Prog

(PARI) a(n)=my(k=n, s); while(k>1, k=if(k%2, 3*k+1, k/2); if(k>n, s++)); s \\ Charles R Greathouse IV, Aug 26 2016

Crossrefs

Cf. A033496, A213199 (location of zero and nonzero terms).

Sequence in context: A172035 A019625 A261165 * A021999 A021203 A276712

Adjacent sequences: A222594 A222595 A222596 * A222598 A222599 A222600

Keyword

nonn

Author

T. D. Noe, Mar 01 2013

Status

approved