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
From Andrew Slattery, Aug 03 2023: (Start)
For most terms k, the trajectory of 3k + 1 reaches 310 or the trajectory of 310 reaches k.
For the rest of the terms k, the trajectory of 3k + 1 reaches 22 or the trajectory of 22 reaches k.
With the exception of k = 1, k is reached after S steps,
where S = c*8 + d*13 + e*44 + f*75, with c, d, e and f in {0, 1, 2}; in particular, S is in {8, 13, 8+8, 8+13, 13+13, 44, 75, 44+44, 75+13+13, 75+44, 75+75}. (End)
LINKS
Eric Weisstein's World of Mathematics, Collatz Problem
Wikipedia, Collatz conjecture
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 !! (n-1)
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 Fröhlich, Jun 10 2021
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
Robert C. Lyons, Nov 25 2012
EXTENSIONS
Initial 1 from Clark R. Lyons, Dec 02 2012
STATUS
approved