

A219696


Numbers k such that the trajectory of 3k + 1 under the '3x + 1' map reaches k.


2



1, 2, 4, 8, 10, 14, 16, 20, 22, 26, 40, 44, 52, 106, 184, 206, 244, 274, 322, 526, 650, 668, 790, 866, 976, 1154, 1300, 1438, 1732, 1780, 1822, 2308, 2734, 3238, 7288
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This sequence seems complete; there are no other terms <= 10^9.  T. D. Noe, Dec 03 2012
If the 3x+1 step is replaced with (3x+1)/2, the sequence becomes {1, 2, 4, 8, 10, 14, 20, 22, 26, 40, 44, 206, 244, 650, 668, 866, 1154, 1822, 2308, ...}.  Robert G. Wilson v, Jan 13 2015


LINKS

Table of n, a(n) for n=1..35.
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem


EXAMPLE

For k = 4, the Collatz trajectory of 3k + 1 is (13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which includes 4; thus, 4 is in the sequence.
For k = 5, the Collatz trajectory of 3k + 1 is (16, 8, 4, 2, 1), which does not include 5; thus, 5 is not in the sequence.


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[10000], MemberQ[Collatz[3 # + 1], #] &] (* T. D. Noe, Dec 03 2012 *)


PROG

(Haskell)
a219696 n = a219696_list !! (n1)
a219696_list = filter (\x > collatz'' x == x) [1..] where
collatz'' x = until (`elem` [1, x]) a006370 (3 * x + 1)
 Reinhard Zumkeller, Aug 11 2014
(Python)
def ok(n):
if n==1: return [1]
N=3*n + 1
l=[N, ]
while True:
if N%2==1: N = 3*N + 1
else: N/=2
l+=[N, ]
if N<2: break
if n in l: return 1
return 0 # Indranil Ghosh, Apr 22 2017
(PARI) a006370(n) = if(n%2==0, n/2, 3*n+1)
is(n) = my(x=3*n+1); while(1, x=a006370(x); if(x==n, return(1), if(x==1, return(0)))) \\ Felix FrÃ¶hlich, Jun 10 2021


CROSSREFS

Cf. A014682, A070991, A006370, A070165.
Sequence in context: A047235 A328588 A287844 * A087505 A086801 A154115
Adjacent sequences: A219693 A219694 A219695 * A219697 A219698 A219699


KEYWORD

nonn,nice,more


AUTHOR

Robert C. Lyons, Nov 25 2012


EXTENSIONS

Initial 1 from Clark R. Lyons, Dec 02 2012


STATUS

approved



