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A258056 3x + 1 sequence starting at 75.

%I A258056 #41 Sep 08 2022 08:46:12
%S A258056 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,
%T A258056 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,
%U A258056 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
%N A258056 3x + 1 sequence starting at 75.
%C A258056 a(n) gives the value obtained after n iterations of the Collatz function starting at 75. - _Daniel Forgues_, May 19 2015
%C A258056 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
%H A258056 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A258056 a(0) = 75; a(n) = 3*a(n - 1) + 1 if a(n - 1) is odd, a(n) = a(n - 1)/2 otherwise.
%e A258056 75 is odd, so it's followed by 3*75 + 1 = 226.
%e A258056 226 is even, so it's followed by 226/2 = 113.
%t A258056 NestList[If[EvenQ[#], #/2, 3# + 1] &, 75, 100]
%o A258056 (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
%o A258056 (Sage)
%o A258056 def collatz(start):
%o A258056     a = start
%o A258056     while True:
%o A258056         yield a
%o A258056         a = 3*a + 1 if is_odd(a) else a/2
%o A258056 A258056 = collatz(75)
%o A258056 [next(A258056) for _ in range(60)] # _Peter Luschny_, May 22 2015
%Y A258056 Cf. A033478, A153727.
%Y A258056 Row 75 of A347270.
%K A258056 nonn,easy
%O A258056 0,1
%A A258056 _Alonso del Arte_, May 17 2015