cp's OEIS Frontend

A288311 Number of steps, reduced mod n, to reach 1 in the Collatz 3x+1 problem, or -1 if 1 is never reached.

%I A288311 #17 Oct 27 2024 20:29:09
%S A288311 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 A288311 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 A288311 2,19,32,19,32,19,19,45,44,6,27,27,27,14,14,14,31,22
%N A288311 Number of steps, reduced mod n, to reach 1 in the Collatz 3x+1 problem, or -1 if 1 is never reached.
%F A288311 a(n) = A006577(n) mod n.
%e A288311 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 A288311 Table[Mod[-1 + Length[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &]], n], {n, 72}] (* _Michael De Vlieger_, Jun 09 2017 *)
%o A288311 (Python)
%o A288311 def stepCount(x):
%o A288311     x = int(x)
%o A288311     steps = 0
%o A288311     while True:
%o A288311         if x == 1:
%o A288311             break
%o A288311         elif x % 2 == 0:
%o A288311             x = x/2
%o A288311             steps += 1
%o A288311         else:
%o A288311             x = x*3 + 1
%o A288311             steps += 1
%o A288311     return steps
%o A288311 n = 1
%o A288311 while True:
%o A288311     print(stepCount(n) % n)
%o A288311     n += 1
%o A288311 (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 A288311 Cf. A006577.
%K A288311 nonn
%O A288311 1,4
%A A288311 _Ryan Pythagoras Newton Critchlow_, Jun 07 2017