A181762 a(n) = n/2 if n is even, otherwise 3n+5.

0, 8, 1, 14, 2, 20, 3, 26, 4, 32, 5, 38, 6, 44, 7, 50, 8, 56, 9, 62, 10, 68, 11, 74, 12, 80, 13, 86, 14, 92, 15, 98, 16, 104, 17, 110, 18, 116, 19, 122, 20, 128, 21, 134, 22, 140, 23, 146, 24, 152, 25, 158, 26, 164, 27, 170, 28, 176, 29, 182, 30, 188, 31, 194, 32, 200, 33, 206, 34, 212, 35, 218, 36, 224, 37

Offset: 0

Author

N. J. A. Sloane, Jan 31 2011

Keywords

• nonn
• easy

Comments

Has at least two periodic orbits, {1,8,4,2} and {5,20,10}.

Four others are {19,62,31,98,49,152,76,38}, {23,74,37,116,58,29,92,46}, {187,...} and {347,...}. The last two are each of length 44, peaking with 8324 and 10196 respectively. - Geoffrey H. Morley, Mar 14 2013

References

• J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010. See p. 307.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A006370.

Programs

Magma

[(7*n+10-10*(-1)^n*(n/2+1))/4: n in [0..80]]; // Vincenzo Librandi, May 24 2011

Maple

f:=n->if n mod 2 = 0 then n/2 else 3*x+5 fi;

Mathematica

Table[If[EvenQ[n],n/2,3n+5],{n,0,80}] (* Harvey P. Dale, Nov 25 2023 *)

Formula

G.f.: -x*(-8 - x + 2*x^2) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Mar 10 2011