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%I #13 Jun 16 2017 22:41:59
%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 3)
%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
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