A340420 The number of steps that n requires to reach 1 under the map: m -> m/2 if m is even, m-> 3*m + 1 if m is an odd prime, otherwise m -> m - 1. a(n) = -1 if 1 is never reached.

0, 1, 7, 2, 5, 8, 16, 3, 4, 6, 14, 9, 9, 17, 18, 4, 12, 5, 20, 7, 8, 15, 16, 10, 11, 10, 11, 18, 18, 19, 19, 5, 6, 13, 14, 6, 21, 21, 22, 8, 22, 9, 9, 16, 17, 17, 17, 11, 12, 12, 13, 11, 11, 12, 13, 19, 20, 19, 32, 20, 20, 20, 21, 6, 7, 7, 27, 14, 15, 15, 15

Offset

1,3

Comments

Conjecture: a(n) is never equal to -1.

Links

Table of n, a(n) for n=1..71.

Example

a(3) = 7 because 3*3 + 1 = 10 -> 10/2 = 5 -> 3*5 + 1 = 16 -> 16/2 = 8 -> 8/2 = 4 -> 4/2 = 2 -> 2/2 = 1 -> 1.
a(14) = 17 because 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.
The 39 terms for a(n) <= 9 are given in the figure below.
145 288 12 42 13 80 133 264 260 258 255 512
  \  /   \  \  \ /    \ /    |   |   \  /
   144    6  21 40    132   130 129  256
     \     \   \ |     |     |    \  /
      72    3   20     66    65   128
        \     \ /       \     \   /
         36    10       33      64
           \     \        \    /
            18     5        32
               \     \     /
                 9      16
                   \    /
                      8
                      |
                      4
                      |
                      2
                      |
                      1

Maple

a:= proc(n) option remember; `if`(n=1, 0, 1 + a(
     `if`(n::even, n/2, `if`(isprime(n), 3*n+1, n-1))))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 08 2021

Mathematica

a[n_] := a[n] = If[n == 1, 0, 1 + a[
   If[EvenQ[n], n/2, If[PrimeQ[n], 3n+1, n-1]]]];
Array[a, 100] (* Jean-François Alcover, Jan 30 2021, after Alois P. Heinz *)

Prog

(Python)
from sympy import isprime
for n in range(1, 101):
    ct, m = 0, n
    while m > 1:
        if m%2 == 0: m /= 2
        elif isprime(m) == 1: m = 3*m + 1
        else: m -= 1
        ct += 1
    print(ct)
(PARI) f(n) = if (n % 2, if (isprime(n), 3*n+1, n-1), n/2);
a(n) = my(s=n, c=0); while(s>1, s=f(s); c++); c; \\ Michel Marcus, Jan 21 2021

Crossrefs

Cf. A006577, A060413, A339991, A340008, A340418.

Sequence in context: A200237 A072761 A337357 * A127885 A006577 A337150

Adjacent sequences: A340417 A340418 A340419 * A340421 A340422 A340423

Keyword

nonn

Author

Ya-Ping Lu, Jan 07 2021

Status

approved