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

%I A340594 #8 Jan 14 2021 18:12:30
%S A340594 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 A340594 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 A340594 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 A340594 a(n) is the number of iterations of A340592 starting from n, until 0, 1 or a prime is reached.
%C A340594 a(n) = 0 if n is prime.
%H A340594 Robert Israel, <a href="/A340594/b340594.txt">Table of n, a(n) for n = 2..10000</a>
%F A340594 a(n) = A066247(n)*(1 + a(A340592(n))).
%e A340594 A340592(21) = 16, A340592(16) = 14, A340592(14) = 13 is prime, so a(21) = 3.
%p A340594 dcat:= proc(L) local i, x;
%p A340594   x:= L[-1];
%p A340594   for i from nops(L)-1 to 1 by -1 do
%p A340594     x:= 10^(1+ilog10(x))*L[i]+x
%p A340594   od;
%p A340594   x
%p A340594 end proc:
%p A340594 f:= proc(n) local F;
%p A340594   F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);
%p A340594   dcat(map(t -> t[1]$t[2], F)) mod n;
%p A340594 end proc:
%p A340594 g:= proc(n) option remember;
%p A340594      if isprime(n) then 0 else 1 + procname(f(n)) fi
%p A340594 end proc:
%p A340594 g(0):= 0: g(1):= 0:
%p A340594 map(g, [$1..1000]);
%Y A340594 Cf. A066247, A340592, A340595.
%K A340594 nonn
%O A340594 2,7
%A A340594 _J. M. Bergot_ and _Robert Israel_, Jan 13 2021