A383777 a(n) is the number of steps that n requires to reach 0 under the map: x -> 2*x + 1 if x is even; 0 if x = 1; x - lpf(x) otherwise where lpf(x) is the least prime factor of x. a(n) = -1 if 0 is never reached.

0, 1, 2, 1, 4, 1, 2, 1, 2, 3, 4, 1, 4, 1, 2, 5, 4, 1, 2, 1, 2, 3, 10, 1, 10, 3, 2, 11, 4, 1, 2, 1, 10, 3, 12, 3, 2, 1, 6, 3, 4, 1, 8, 1, 2, 9, 4, 1, 2, 9, 2, 3, 6, 1, 2, 3, 2, 3, 4, 1, 8, 1, 4, 9, 10, 9, 10, 1, 2, 11, 4, 1, 4, 1, 2, 5, 10, 5, 2, 1, 6, 3, 6, 1

Offset

0,3

Comments

Conjecture: a(n) != -1.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Example

a(10) = 4 because it takes 4 steps for 10 to reach 1 by iterating the map: 10 -> 2*10+1=21 -> 21-3=18 -> 2*18+1=37 -> 37-37=0.

Mathematica

A383777[n_] := Length[NestWhileList[If[OddQ[#], # - FactorInteger[#][[1, 1]], 2*# + 1] &, n, # >0 &]] - 1;
Array[A383777, 100, 0] (* Paolo Xausa, May 22 2025 *)

Prog

(Python)
from sympy import primefactors; mp = lambda x: (0 if x ==1 else x - min(primefactors(x)) if x%2 else 2*x+1)
def A383777(n, c = 0):
    while n != 0: n = mp(n); c += 1
    return c

Crossrefs

Cf. A005408, A006577, A046666.

Sequence in context: A057550 A324892 A379704 * A059150 A087230 A133186

Adjacent sequences: A383774 A383775 A383776 * A383778 A383779 A383780

Keyword

nonn

Author

Ya-Ping Lu, May 17 2025

Status

approved