A072466 Numbers with 11 odd integers in their Collatz (or 3x+1) trajectory.

57, 59, 114, 115, 118, 119, 228, 229, 230, 236, 237, 238, 456, 458, 460, 461, 465, 472, 473, 474, 476, 477, 507, 513, 912, 916, 917, 920, 922, 930, 931, 943, 944, 945, 946, 947, 948, 949, 952, 954, 971, 987, 1014, 1015, 1025, 1026, 1027, 1031, 1129, 1131

Offset: 1

Author

Jim Nastos, Jun 19 2002

Keywords

• easy
• nonn

Comments

The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd. The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.

References

• J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A062052-A062060.

Column k=11 of A354236.

Programs

Maple

b:= proc(n) option remember; irem(n, 2, 'r')+
      `if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))
    end:
q:= n-> is(b(n)=11):
select(q, [$1..2000])[];  # Alois P. Heinz, May 18 2022

Mathematica

ocollQ[n_]:=Length[Select[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],OddQ[#]&]]==11; Select[Range[1140],ocollQ[#]&] (* Jayanta Basu, May 28 2013 *)