A288311 - OEIS

%I #17 Oct 27 2024 20:29:09

%S 0,1,1,2,0,2,2,3,1,6,3,9,9,3,2,4,12,2,1,7,7,15,15,10,23,10,3,18,18,18,

%T 13,5,26,13,13,21,21,21,34,8,27,8,29,16,16,16,10,11,24,24,24,11,11,4,

%U 2,19,32,19,32,19,19,45,44,6,27,27,27,14,14,14,31,22

%N Number of steps, reduced mod n, to reach 1 in the Collatz 3x+1 problem, or -1 if 1 is never reached.

%F a(n) = A006577(n) mod n.

%e For n = 3, which takes 7 steps to reach 1 in the Collatz (3x+1) problem: (10, 5, 16, 8, 4, 2, 1), 7 mod 3 = 1.

%t Table[Mod[-1 + Length[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &]], n], {n, 72}] (* _Michael De Vlieger_, Jun 09 2017 *)

%o (Python)

%o def stepCount(x):

%o     x = int(x)

%o     steps = 0

%o     while True:

%o         if x == 1:

%o             break

%o         elif x % 2 == 0:

%o             x = x/2

%o             steps += 1

%o         else:

%o             x = x*3 + 1

%o             steps += 1

%o     return steps

%o n = 1

%o while True:

%o     print(stepCount(n) % n)

%o     n += 1

%o (PARI) a(n)=s=n; c=0; while(s>1, s=if(s%2, 3*s+1, s/2); c++); c % n; \\ _Michel Marcus_, Jun 10 2017

%Y Cf. A006577.

%K nonn

%O 1,4

%A _Ryan Pythagoras Newton Critchlow_, Jun 07 2017