A222292 - OEIS

%I #40 Oct 31 2024 01:16:15

%S 1,2,3,3,3,7,15,15,27,27,27,27,27,27,447,447,703,703,1819,1819,1819,

%T 4255,4255,9663,9663,20895,26623,60975,60975,60975,77671,113383,

%U 159487,159487,159487,665215,1042431,1212415,2684647,3041127,4637979,5656191,6416623

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

%C Are the unique values a subset of A006884? - _Ralf Stephan_, May 27 2013

%C 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.

%H T. D. Noe, <a href="/A222292/b222292.txt">Table of n, a(n) for n = 0..63</a>

%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/pathrecs.html">3x+1 path records</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%p b:= proc(n) option remember; `if`(n=1, 1,

%p       max(n, b(`if`(n::even, n/2, 3*n+1))))

%p     end:

%p a:= proc(n) option remember; local i, t; t:=2^n;

%p       for i while b(i)<t do od: i

%p     end:

%p seq(a(n), n=0..38);  # _Alois P. Heinz_, Sep 25 2024

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

%Y Cf. A095384.

%K nonn,base,changed

%O 0,2

%A _T. D. Noe_, Feb 19 2013

%E a(1) corrected by _Kevin Ge_, Sep 25 2024