

A302858


3x + 1 sequence beginning at 13.


0



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
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OFFSET

0,1


COMMENTS

The 3x + 1 problem remains unsolved. But the 3x + 1 problem is easy to answer definitively: none of the thirtyone 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(n1)) select 3*Self(n1)+1 else Self(n1) 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



