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A288311
Number of steps, reduced mod n, to reach 1 in the Collatz 3x+1 problem, or -1 if 1 is never reached.
0
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
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
KEYWORD
nonn,changed
AUTHOR
STATUS
approved