A033481 3x+1 sequence beginning at 21.

21, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1

Offset: 0

Author

Jeff Burch

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Bertrand Teguia Tabuguia, Hypergeometric-Type Sequences, arXiv:2401.00256 [cs.SC], 2023. See p. 20.
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Row 21 of A347270.

Programs

Mathematica

NestList[If[EvenQ[#],#/2,3#+1]&,21,100] (* or *) PadRight[ {21,64,32,16,8},100,{2,1,4}] (* Harvey P. Dale, Sep 30 2018 *)

PARI

Vec((21 + 64*x + 32*x^2 - 5*x^3 - 56*x^4 - 28*x^5 - 14*x^6 - 7*x^7) / ((1 - x)*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Oct 04 2019

Formula

From Colin Barker, Oct 04 2019: (Start)

G.f.: (21 + 64*x + 32*x^2 - 5*x^3 - 56*x^4 - 28*x^5 - 14*x^6 - 7*x^7) / ((1 - x)*(1 + x + x^2)).

a(n) = a(n-3) for n>15.

(End)