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

1,4

Links

Table of n, a(n) for n=1..72.

Formula

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

Example

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.

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A006577.

Sequence in context: A293665 A159632 A164733 * A244366 A262676 A070101

Adjacent sequences: A288308 A288309 A288310 * A288312 A288313 A288314

Keyword

nonn

Author

Ryan Pythagoras Newton Critchlow, Jun 07 2017

Status

approved