A381329 Number of steps for n to reach 1 under the map x -> x/2 if x is even, x -> 2*x+1 if x is prime or a perfect power, otherwise x -> gpf(x)-1 where gpf(x) = A006530(x).

0, 1, 5, 2, 16, 6, 4, 3, 10, 17, 15, 7, 20, 5, 3, 4, 8, 11, 9, 18, 7, 16, 14, 8, 6, 21, 19, 6, 7, 4, 8, 5, 18, 9, 7, 12, 4, 10, 8, 19, 23, 8, 8, 17, 3, 15, 13, 9, 19, 7, 5, 22, 11, 20, 18, 7, 12, 8, 6, 5, 21, 9, 7, 6, 8, 19, 4, 10, 17, 8, 9, 13, 8, 5, 3, 11, 18

Offset

1,3

Comments

Does every n reach 1?

Links

Table of n, a(n) for n=1..77.

Example

n=7 reaches 1 by 7 -> 15 -> 4 -> 2 -> 1 which is a(7)=4 steps.
Starting from 47993 yields 4362, 2181, 726, 363, 10, 5, 11, 23, 47, 95, 18, 9, 19, 39, 12, 6, 3, 7, 15, 4, 2, 1. Thus a(47993)=22.

Mathematica

s[n_] := Which[n == 1, 1, EvenQ[n], n/2, PrimeQ[n] || GCD @@ ((f = FactorInteger[n])[[;; , 2]]) > 1, 2*n + 1, True, f[[-1, 1]] - 1]; a[n_] := -1 + Length@ NestWhileList[s, n, # > 1 &]; Array[a, 100] (* Amiram Eldar, Feb 20 2025 *)

Crossrefs

Cf. A006530.

Sequence in context: A297979 A298630 A248258 * A279150 A213582 A364108

Adjacent sequences: A381326 A381327 A381328 * A381330 A381331 A381332

Keyword

nonn,new

Author

Bill McEachen, Feb 20 2025

Status

approved