A222291 -id:A222291 - cp's OEIS frontend

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

T. D. Noe, Feb 19 2013

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.

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

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

Cf. A095384.

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

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

A224538 Number of numbers k such that all terms of the Collatz (3x+1) iteration of k are <= 10^n.

Original entry on oeis.org

1, 4, 49, 340, 4235, 39706, 397068, 3970918, 39523168, 395436300, 3953296865

Offset: 0

T. D. Noe, Apr 24 2013

			For n = 1, the four k are 1, 2, 4, and 8.

Cf. A006884, A006885, A095384, A222291, A224540.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Select[Range[10^n], Max[Collatz[#]] <= 10^n &]], {n, 0, 5}]

a(10) from Donovan Johnson, Jun 05 2013

cp's OEIS Frontend

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

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