A359207 Number of steps to reach 0 starting with n in the map x->A359194(x) (binary complement of 3n), or -1 if 0 is never reached.

0, 1, 2, 11, 12, 1, 10, 3, 4, 13, 2, 19, 80, 9, 2, 15, 16, 81, 14, 11, 12, 1, 6, 83, 8, 73, 22, 79, 7572, 5, 18, 75, 76, 7573, 74, 7, 12, 17, 10, 3, 4, 13, 2, 7571, 4, 85, 78, 15, 96, 21, 5498, 91, 72, 13, 6, 7, 56, 13, 82, 3, 20, 5, 98, 15, 16, 21, 14, 7

Offset

0,3

Comments

It is unknown whether each positive starting integer eventually reaches 0.

From Jon E. Schoenfield, Dec 21 2022: (Start)

a(n) == n (mod 4).

a(n) = 1 iff 3*n + 1 = 4^k for some integer k. (End)

All but 10 values under 10^7 have been run to 0. Each of the remaining 10 requires over 2*10^12 steps. They're all in one group that reaches the same high value (nearly 8 million bits wide) after about 2*10^12 steps. The smallest value in this group is 3417582. - Tim Peters, Jun 14 2023

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Tim Peters, Seeds under 2*10^6 that take more than 10^8 steps to reach 0

Tim Peters, Seeds under 10^7 that take more than 10^9 steps to reach 0

Joshua Searle, Collatz-inspired sequences.

Example

a(7) = 3 because it takes 3 steps to reach 0: (7, 10, 1, 0).

Mathematica

f[n_] := FromDigits[BitXor[1, IntegerDigits[3*n, 2]], 2]; Array[-1 + Length@ NestWhileList[f, #, # != 0 &] &, 68, 0] (* Michael De Vlieger, Dec 21 2022, faster function by Hans Havermann *)

Prog

(Python)
def f(n): return 1 if n == 0 else (m:=3*n)^((1 << m.bit_length())-1)
def a(n):
    i, fi = 0, n
    while fi != 0: i, fi = i+1, f(fi)
    return i
print([a(n) for n in range(68)]) # Michael S. Branicky, Dec 20 2022
(PARI) f(n) = if(n, bitneg(n, exponent(n)+1), 1); \\ A035327
a(n) = my(nb=0, m=n); while (m, m=f(3*m); nb++); nb; \\ Michel Marcus, Dec 21 2022

Crossrefs

Cf. A035327, A359194, A359208, A359209, A359255.

Sequence in context: A090009 A153706 A201187 * A068225 A367810 A043080

Adjacent sequences: A359204 A359205 A359206 * A359208 A359209 A359210

Keyword

nonn,base

Author

Joshua Searle, Dec 20 2022

Status

approved