A008896 3x - 1 sequence starting at 66.

66, 33, 98, 49, 146, 73, 218, 109, 326, 163, 488, 244, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136, 68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

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

Links

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

Crossrefs

Cf. A008880 (3x + 1 sequence starting at 33).

Programs

Mathematica

NestList[If[EvenQ[#], #/2, 3# - 1] &, 66, 50] (* or *) PadRight[ {66, 33, 98, 49, 146, 73, 218, 109, 326, 163, 488, 244}, 120, {68, 34, 17, 50, 25, 74, 37, 110, 55, 164, 82, 41, 122, 61, 182, 91, 272, 136}] (* Harvey P. Dale, Sep 02 2018 *)

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.map( * -1) // _Alonso del Arte, Apr 25 2020

Formula

a(0) = 66, a(n) = a(n - 1)/2 if a(n - 1) is even, otherwise 3a(n - 1) - 1.

Extensions

More specific name from Alonso del Arte, Apr 25 2020 (was "x -> x/2 if x even, x -> 3x - 1 if x odd").