A383131 - OEIS

A383131

a(n) is the number of iterations that n requires to reach 1 under the map x -> -x/2 if x is even, 3x + 1 if x is odd; a(n) = -1 if 1 is never reached.

0, 3, 12, 2, 5, 5, 8, 5, 11, 11, 50, 14, 14, 14, 53, 4, 17, 17, 43, 7, 7, 7, 20, 7, 46, 46, 59, 10, 10, 10, 23, 7, 49, 49, 62, 13, 13, 13, 13, 13, 26, 26, 39, 52, 52, 52, 65, 16, 16, 16, 78, 16, 16, 16, 29, 16, 42, 42, 55, 55, 55, 55, 68, 6, 19, 19, 19, 19, 19

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OFFSET

1,2

COMMENTS

A plot of a(n) for non-zero integers n in the range of (-10000, 10000) is given in LINKS.

Conjecture: a(n) != -1 for any positive or negative integer n.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Ya-Ping Lu, A plot of a(n) for n in the range of (-10000, 10000)

EXAMPLE

a(3) = 12 because it takes 12 steps for n = 3 to reach 1: 3 -> 10 -> -5 -> -14 -> 7 -> 22 -> -11 -> -32 -> 16 -> -8 -> 4 -> -2 -> 1.

MAPLE

a:= proc(n) option remember; `if`(n=1, 0,

1+a(`if`(n::even, -n/2, 3*n+1)))

end:

seq(a(n), n=1..69); # Alois P. Heinz, Aug 13 2025

MATHEMATICA

js[n_] := If[EvenQ[n], -n/2, 3n+1]; f[n_] := Length[ NestWhileList[js, n, # != 1 &]] - 1; Table[ f[n], {n, 69}] (* James C. McMahon, Apr 30 2025 *)

PROG

(Python)

def A383131(n):

ct = 0

while n != 1: n = 3*n+1 if n%2 else -n>>1; ct += 1

return ct

(PARI) a(n) = { for (k = 0, oo, if (n==1, return (k), n = if (n%2, 3*n+1, -n/2)); ); } \\ Rémy Sigrist, Apr 19 2025

CROSSREFS

Cf. A006577, A381055.

Sequence in context: A342787 A110121 A321710 * A358325 A288518 A069522

Adjacent sequences: A383128 A383129 A383130 * A383132 A383133 A383134

KEYWORD

nonn

AUTHOR

Ya-Ping Lu, Apr 17 2025

STATUS

approved