A008894 3x - 1 sequence starting at 36.

36, 18, 9, 26, 13, 38, 19, 56, 28, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20

Offset

0,1

Comments

Previous name was "x -> x/2 if x even, x -> 3x - 1 if x odd."

References

R. K. Guy, Unsolved Problems in Number Theory, E16.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Formula

a(0) = 36, a(n) = a(n - 1)/2 if a(n - 1) is even, otherwise 3a(n - 1) - 1.

From Colin Barker, Apr 26 2020: (Start)

G.f.: (36 + 18*x + 9*x^2 + 26*x^3 + 13*x^4 + 2*x^5 + x^6 + 47*x^7 + 2*x^8 + x^9 - 31*x^10 + x^11 - 46*x^12 - 23*x^13) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n - 5) for n > 13.

(End)

Mathematica

-NestList[If[EvenQ[#], #/2, 3# + 1] &, -36, 100] (* Alonso del Arte, Apr 26 2020 *)

Prog

(Scala) def collatz(n: Int): Int = n % 2 match {
  case 0 => n / 2
  case _ => 3 * n + 1
}
def collatzSeq(n: Int): LazyList[Int] = LazyList.iterate(n)(collatz)
collatzSeq(-36).take(100).toList.map(_ * -1) // Alonso del Arte, Apr 26 2020
(PARI) Vec((36 + 18*x + 9*x^2 + 26*x^3 + 13*x^4 + 2*x^5 + x^6 + 47*x^7 + 2*x^8 + x^9 - 31*x^10 + x^11 - 46*x^12 - 23*x^13) / ((1 - x)*(1 + x + x^2 + x^3 + x^4)) + O(x^70)) \\ Colin Barker, Apr 26 2020

Crossrefs

Sequence in context: A056770 A061038 A058231 * A033973 A033356 A158955

Adjacent sequences: A008891 A008892 A008893 * A008895 A008896 A008897

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More specific name from Alonso del Arte, Apr 26 2020

Status

approved