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

Author

T. D. Noe, Mar 01 2013

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Mathematica

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

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