A302858 -3x + 1 sequence beginning at 13.

13, -38, -19, 58, 29, -86, -43, 130, 65, -194, -97, 292, 146, 73, -218, -109, 328, 164, 82, 41, -122, -61, 184, 92, 46, 23, -68, -34, -17, 52, 26, 13, -38, -19, 58, 29, -86, -43, 130, 65, -194, -97, 292, 146, 73, -218, -109, 328, 164, 82, 41, -122, -61, 184, 92, 46, 23, -68, -34, -17

Offset

0,1

Comments

The 3x + 1 problem remains unsolved. But the -3x + 1 problem is easy to answer definitively: none of the thirty-one numbers in this sequence reach 1 because they form a cycle that does not include 1.

Links

Table of n, a(n) for n=0..59.

Formula

a(0) = 13; a(n) = (-3)*a(n - 1) + 1 if a(n - 1) is odd, a(n) = a(n - 1)/2 otherwise.

Example

13 is odd, so it's followed by (-3) * 13 + 1 = -39 + 1 = -38.
-38 is even, so it's followed by -38/2 = -19.

Mathematica

NestList[If[EvenQ[#], #/2, -3# + 1] &, 13, 100]

Prog

(Magma) [n eq 1 select 13 else IsOdd(Self(n-1)) select -3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // Vincenzo Librandi, Jun 11 2018

Crossrefs

Sequence in context: A309808 A201809 A129541 * A244185 A044090 A044471

Adjacent sequences: A302855 A302856 A302857 * A302859 A302860 A302861

Keyword

sign,easy

Author

Alonso del Arte, May 26 2018

Status

approved