A288569 Start with n and repeatedly apply the map x -> A087207(x) until we reach 0; a(n) is the number of steps needed, or -1 if 0 is never reached.

1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 5, 2, 3, 4, 3, 4, 5, 4, 3, 4, 3, 6, 3, 4, 3, 4, 3, 2, 5, 6, 5, 4, 3

Offset

1,2

Comments

There is a conjecture that 0 is always reached - see A087207.

Links

Table of n, a(n) for n=1..37.

Robert Israel, Table of n, a(n) for n = 1..10000. If a(n) is not known, it is given in the form k + a(x). [A large file]

Example

10 -> 5 -> 4 -> 1 -> 0 reaches 0 in 4 steps, so a(10)=4.
38 = 2*19 -> 129 = 3*43 -> 8194 = 2*17*241 -> 4503599627370561 = 3^2*37*71*190483425427 -> ..., and a(38) is presently unknown.

Maple

f:= proc(n) local i; option remember;
  add(2^(numtheory:-pi(t)-1), t = numtheory:-factorset(n)) end proc:
g:= proc(n) local t, count;
   t:= n;
   for count from 0 while t <> 0 do
      t:= f(t)
   od;
   count
end proc:
map(g, [$1..37]); # Robert Israel, Jun 25 2017

Mathematica

f[n_] := Total[2^(PrimePi /@ FactorInteger[n][[All, 1]]-1)]; f[1] = 0;
g[n_] := Module[{t, count}, t = n; For[count = 0, t != 0, count++, t = f[t]]; count];
Table[g[n], {n, 1, 37}] (* Jean-François Alcover, Aug 15 2023, after Robert Israel *)

Prog

(Python)
from sympy import factorint, primepi
def f(n):
    return 0 if n < 2 else sum(1 << int(primepi(i-1)) for i in factorint(n))
def a(n):
    fn, c = n, 0
    while not fn == 0: fn, c = f(fn), c+1
    return c
print([a(n) for n in range(1, 38)]) # Michael S. Branicky, Jul 11 2022

Crossrefs

Cf. A087207.

Sequence in context: A175794 A324389 A105500 * A088748 A323235 A086374

Adjacent sequences: A288566 A288567 A288568 * A288570 A288571 A288572

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Jun 25 2017

Status

approved