A340594 a(n) is the number of iterations of A340592 starting from n, until 0, 1 or a prime is reached.

0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 3, 1, 0, 2, 1, 1, 3, 1, 0, 2, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 0, 4, 0, 1, 2, 2, 0, 1, 2, 1, 1, 1, 0, 1, 3, 1, 2, 4, 0, 2, 0, 3, 2, 2, 5, 1, 0, 1, 1, 1, 0, 3, 0, 2, 4, 2, 2, 2, 0, 6, 2, 3, 0, 1, 1, 1, 2, 3, 0, 2, 3, 2, 2, 1, 2, 1, 0, 3, 2

Offset: 2

Author

J. M. Bergot and Robert Israel, Jan 13 2021

Keywords

• nonn

Comments

a(n) = 0 if n is prime.

Examples

			A340592(21) = 16, A340592(16) = 14, A340592(14) = 13 is prime, so a(21) = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A066247, A340592, A340595.

Programs

Maple

dcat:= proc(L) local i, x;
  x:= L[-1];
  for i from nops(L)-1 to 1 by -1 do
    x:= 10^(1+ilog10(x))*L[i]+x
  od;
  x
end proc:
f:= proc(n) local F;
  F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);
  dcat(map(t -> t[1]$t[2], F)) mod n;
end proc:
g:= proc(n) option remember;
     if isprime(n) then 0 else 1 + procname(f(n)) fi
end proc:
g(0):= 0: g(1):= 0:
map(g, [$1..1000]);

Formula

a(n) = A066247(n)*(1 + a(A340592(n))).