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

1, 3, 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

0,2

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 31-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

Mathematica

mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#], #/2, 3#+1] &, n, #>1 &]; i=1; Join[{1, 3}, Table[i=i; While[mcoll[i]<2^n, i=i+2]; i, {n, 2, 30}]] (* Jayanta Basu, May 27 2013 *)

Crossrefs

Cf. A222291 (base-10 version).

Cf. A095384.

Sequence in context: A098528 A242715 A078229 * A245441 A333793 A007428

Adjacent sequences: A222289 A222290 A222291 * A222293 A222294 A222295

Keyword

nonn,base

Author

T. D. Noe, Feb 19 2013

Status

approved