A008880 3x + 1 sequence starting at 33.

33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 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

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

Index entries for sequences related to 3x+1 (or Collatz) problem

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

Maple

f := proc(n) option remember; if n = 0 then 33; 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] &, 33, 100] (* Vincenzo Librandi, Jul 29 2014 *)

Prog

(Magma) [n eq 1 select 33 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // 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(33).take(100).toList // Alonso del Arte, Apr 25 2020

Crossrefs

Cf. similar sequences listed in A245671.

Cf. A008896 (3x - 1 sequence starting at 66).

Row 33 of A347270.

Sequence in context: A032650 A284986 A133901 * A370481 A045613 A033574

Adjacent sequences: A008877 A008878 A008879 * A008881 A008882 A008883

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved