A370394 Number of steps to reach 0 by applying the map f(x) = 5x + 1 if x is odd and floor(x/3) if x is even, or -1 if 0 is never reached.

0, 3, 1, 6, 4, 4, 2, 7, 2, 12, 7, 5, 5, 10, 5, 10, 5, 15, 3, 10, 3, 15, 8, 8, 3, 8, 3, 30, 13, 8, 8, 18, 8, 13, 6, 13, 6, 6, 6, 11, 11, 11, 6, 6, 6, 28, 11, 6, 6, 33, 6, 11, 16, 11, 4, 11, 4, 21, 11, 11, 4, 9, 4, 14, 16, 9, 9, 9, 9, 21, 9, 14, 4, 14, 4, 26, 9

Offset

0,2

Comments

Conjecture: for all n, a(n) != -1.

Links

Table of n, a(n) for n=0..76.

Example

For n=3, the trajectory of 3 under map f is as follows and takes a(3) = 6 steps to reach 0: 3 -> 16 -> 5 -> 26 -> 8 -> 2 -> 0.

Maple

a:= proc(n) option remember; `if`(n=0, 0,
      1+a(`if`(n::even, floor(n/3), 5*n+1)))
    end:
seq(a(n), n=0..76);  # Alois P. Heinz, Feb 22 2024

Prog

(Python)
def map_5x(n): return 5*n+1 if n%2 == 1 else n//3
def A370394(n):
    m = n; ct = 0
    while m != 0: m = map_5x(m); ct += 1
    return ct
for n in range(77): print(A370394(n), end = ', ')

Crossrefs

Cf. A002264, A003462, A006577, A016801.

Sequence in context: A116551 A213783 A163330 * A021320 A193864 A066840

Adjacent sequences: A370391 A370392 A370393 * A370395 A370396 A370397

Keyword

nonn

Author

Ya-Ping Lu, Feb 17 2024

Status

approved