A139391 Next odd term in Collatz trajectory with starting value n.

1, 1, 5, 1, 1, 3, 11, 1, 7, 5, 17, 3, 5, 7, 23, 1, 13, 9, 29, 5, 1, 11, 35, 3, 19, 13, 41, 7, 11, 15, 47, 1, 25, 17, 53, 9, 7, 19, 59, 5, 31, 21, 65, 11, 17, 23, 71, 3, 37, 25, 77, 13, 5, 27, 83, 7, 43, 29, 89, 15, 23, 31, 95, 1, 49, 33, 101, 17, 13, 35, 107, 9, 55, 37, 113, 19, 29

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Friedrich L. Bauer, Der (ungerade) Collatz-Baum, Informatik Spektrum 31 (Springer, April 2008).

Eric Weisstein's World of Mathematics, Collatz Problem.

Wikipedia, Collatz conjecture.

Index entries for sequences related to 3x+1 (or Collatz) problem.

Formula

a(n) = A006370(n) if A006370(n) is odd, otherwise a(A006370(n)).

a(n) = A006370(n) iff n mod 4 = 2;

a(A016825(n)) = A006370(A016825(n));

a(n) = A000265(A006370(n)).

a(A160967(n)) = 1. - Reinhard Zumkeller, May 31 2009

For odd n, a(n) = a(2*A350091((n-1)/2)+1). - Ruud H.G. van Tol, Dec 17 2021

Sum_{k=1..n} a(k) ~ n^2 / 3. - Amiram Eldar, Aug 26 2024

Mathematica

a[n_]:=Select[NestWhileList[If[EvenQ[#], #/2, 3#+1] &, n, #>1 &], OddQ]; Prepend[Table[If[EvenQ[n], a[n][[1]], a[n][[2]]], {n, 2, 77}], 1] (* Jayanta Basu, May 27 2013 *)

Prog

(Python) # first formula
def A006370(n): return 3*n+1 if n%2 else n//2
def a(n): return x if (x := A006370(n))%2 else a(x)
print([a(n) for n in range(1, 78)]) # Michael S. Branicky, Dec 15 2021
(Python) # fourth formula, uses A006370 above
def A000265(n):
    while n%2 == 0: n //= 2
    return n
def a(n): return A000265(A006370(n))
print([a(n) for n in range(1, 78)]) # Michael S. Branicky, Dec 15 2021
(PARI) a(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ Michel Marcus, Feb 27 2022

Crossrefs

Cf. A000265, A006370, A016825, A160967, A350091.

Cf. A075677 (odd bisection).

Sequence in context: A179261 A154567 A260210 * A196612 A110635 A179773

Adjacent sequences: A139388 A139389 A139390 * A139392 A139393 A139394

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 17 2008

Status

approved