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

Author

Alonso del Arte, May 17 2015

Keywords

• nonn
• easy

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

Examples

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

Links

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

Crossrefs

Cf. A033478, A153727.

Row 75 of A347270.

Programs

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

Mathematica

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

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

Formula

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