A008876 3x+1 sequence starting at 81.

81, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 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

Offset

0,1

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Darrell Cox, The 3n + 1 Problem: A Probabilistic Approach, Journal of Integer Sequences, Vol. 15 (2012), #12.5.2.

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, Apr 27 2020: (Start)

G.f.: (81 + 244*x + 122*x^2 - 20*x^3 - 60*x^4 - 30*x^5 - 15*x^6 - 161*x^7 - 22*x^8 - 11*x^9 + 83*x^10 - 17*x^11 + 125*x^12 - 26*x^13 - 13*x^14 - 140*x^15 - 70*x^16 - 35*x^17 - 4*x^18 - 2*x^19 - x^20 - 14*x^21 - 7*x^22) / ((1 - x)*(1 + x + x^2)).

a(n) = a(n-3) for n>22.

(End)

Maple

f := proc(n) option remember; if n = 0 then 81; elif f(n-1) mod 2 = 0 then f(n-1)/2 else 3*f(n-1)+1; fi; end;

Mathematica

NestList[If[EvenQ[#], #/2, 3# + 1]&, 81, 100] (* Vincenzo Librandi, Jul 29 2014 *)

Prog

(Haskell)
a008876 n = a008876_list !! n
a008876_list = 81 : iterate a006370 81
-- Reinhard Zumkeller, Aug 30 2012
(Magma) [n eq 1 select 81 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..70]]; // Vincenzo Librandi, Jul 29 2014
(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(81).take(100).toList // Alonso del Arte, Apr 24 2020
(PARI) Vec((81 + 244*x + 122*x^2 - 20*x^3 - 60*x^4 - 30*x^5 - 15*x^6 - 161*x^7 - 22*x^8 - 11*x^9 + 83*x^10 - 17*x^11 + 125*x^12 - 26*x^13 - 13*x^14 - 140*x^15 - 70*x^16 - 35*x^17 - 4*x^18 - 2*x^19 - x^20 - 14*x^21 - 7*x^22) / ((1 - x)*(1 + x + x^2)) + O(x^70)) \\ Colin Barker, Apr 27 2020

Crossrefs

Cf. A006370.

Row 81 of A347270.

Sequence in context: A335843 A255625 A205048 * A031456 A045009 A237167

Adjacent sequences: A008873 A008874 A008875 * A008877 A008878 A008879

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved