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

0,1

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).

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)

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 *)

Prog

(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

Crossrefs

Row 21 of A347270.

Sequence in context: A113781 A299450 A300088 * A041862 A041860 A041864

Adjacent sequences: A033478 A033479 A033480 * A033482 A033483 A033484

Keyword

nonn,easy

Author

Jeff Burch

Status

approved