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A008894 3x - 1 sequence starting at 36. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 07:24 EDT 2020. Contains 337178 sequences. (Running on oeis4.)