A258056 3x + 1 sequence starting at 75.

75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 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, 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

Comments

a(n) gives the value obtained after n iterations of the Collatz function starting at 75. - Daniel Forgues, May 19 2015

a(n) = 1 for the first time with n = 14 (14 iterations); at this point, we get the trivial (1, 4, 2) cycle... (A153727). - Daniel Forgues, May 22 2015

Links

Table of n, a(n) for n=0..90.

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

Formula

a(0) = 75; a(n) = 3*a(n - 1) + 1 if a(n - 1) is odd, a(n) = a(n - 1)/2 otherwise.

Example

75 is odd, so it's followed by 3*75 + 1 = 226.
226 is even, so it's followed by 226/2 = 113.

Mathematica

NestList[If[EvenQ[#], #/2, 3# + 1] &, 75, 100]

Prog

(Magma) [n eq 1 select 75 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..80]]; // Vincenzo Librandi, May 18 2015
(Sage)
def collatz(start):
    a = start
    while True:
        yield a
        a = 3*a + 1 if is_odd(a) else a/2
A258056 = collatz(75)
[next(A258056) for _ in range(60)] # Peter Luschny, May 22 2015

Crossrefs

Cf. A033478, A153727.

Row 75 of A347270.

Sequence in context: A201916 A098230 A348489 * A174685 A158742 A292313

Adjacent sequences: A258053 A258054 A258055 * A258057 A258058 A258059

Keyword

nonn,easy

Author

Alonso del Arte, May 17 2015

Status

approved