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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. similar sequences listed in A245671.

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

Row 33 of A347270.

Programs

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

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 *)

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