A222292 Least number whose Collatz 3x+1 trajectory contains a number >= 2^n.

1, 2, 3, 3, 3, 7, 15, 15, 27, 27, 27, 27, 27, 27, 447, 447, 703, 703, 1819, 1819, 1819, 4255, 4255, 9663, 9663, 20895, 26623, 60975, 60975, 60975, 77671, 113383, 159487, 159487, 159487, 665215, 1042431, 1212415, 2684647, 3041127, 4637979, 5656191, 6416623

Offset: 0

Author

T. D. Noe, Feb 19 2013

Keywords

• nonn
• base

Comments

Are the unique values a subset of A006884? - Ralf Stephan, May 27 2013

This sequence is important for the computation of Collatz numbers. It shows that using 32-bit integers, only numbers less than 159487 can have their Collatz trajectory computed.

Links

• T. D. Noe, Table of n, a(n) for n = 0..63
• Eric Roosendaal, 3x+1 path records
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A025586, A222291 (base-10 version).

Cf. A095384.

Programs

Maple

b:= proc(n) option remember; `if`(n=1, 1,
      max(n, b(`if`(n::even, n/2, 3*n+1))))
    end:
a:= proc(n) option remember; local i, t; t:=2^n;
      for i while b(i)Alois P. Heinz, Sep 25 2024

Extensions

a(1) corrected by Kevin Ge, Sep 25 2024