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

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, 13, 5, 26, 13, 13, 21, 21, 21, 34, 8, 27, 8, 29, 16, 16, 16, 10, 11, 24, 24, 24, 11, 11, 4, 2, 19, 32, 19, 32, 19, 19, 45, 44, 6, 27, 27, 27, 14, 14, 14, 31, 22

Offset: 1

Author

Ryan Pythagoras Newton Critchlow, Jun 07 2017

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A006577.

Programs

Mathematica

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

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

Python

def stepCount(x):
    x = int(x)
    steps = 0
    while True:
        if x == 1:
            break
        elif x % 2 == 0:
            x = x/2
            steps += 1
        else:
            x = x*3 + 1
            steps += 1
    return steps
n = 1
while True:
    print(stepCount(n) % n)
    n += 1

Formula

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