A340594 - OEIS

%I #8 Jan 14 2021 18:12:30

%S 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,

%T 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,

%U 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

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

%C a(n) = 0 if n is prime.

%H Robert Israel, <a href="/A340594/b340594.txt">Table of n, a(n) for n = 2..10000</a>

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

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

%p dcat:= proc(L) local i, x;

%p   x:= L[-1];

%p   for i from nops(L)-1 to 1 by -1 do

%p     x:= 10^(1+ilog10(x))*L[i]+x

%p   od;

%p   x

%p end proc:

%p f:= proc(n) local F;

%p   F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);

%p   dcat(map(t -> t[1]$t[2], F)) mod n;

%p end proc:

%p g:= proc(n) option remember;

%p      if isprime(n) then 0 else 1 + procname(f(n)) fi

%p end proc:

%p g(0):= 0: g(1):= 0:

%p map(g, [$1..1000]);

%Y Cf. A066247, A340592, A340595.

%K nonn

%O 2,7

%A _J. M. Bergot_ and _Robert Israel_, Jan 13 2021