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A340595 a(n) is the least k for which A340594(k) = n.

%I A340595 #5 Jan 14 2021 02:48:03
%S A340595 2,4,8,21,42,65,80,217,488,721,2120,2349,2796,9214,16043,23287,28626,
%T A340595 43588,58176,116982,213435,444329,640673,967248,1399895,1449156,
%U A340595 1528785,2768054,2915135,3631071,3673118,5032731,12977420
%N A340595 a(n) is the least k for which A340594(k) = n.
%C A340595 a(n) is the least k >= 2 from which it takes exactly n iterations of A340592 to reach 0, 1 or a prime.
%e A340595 Starting from 21, it takes 3 iterations of A340592 to reach 0,1 or a prime: 21 -> 16 -> 14 -> 13.  Since this is the first case where 3 iterations are required, a(3) = 21.
%p A340595 dcat:= proc(L) local i, x;
%p A340595   x:= L[-1];
%p A340595   for i from nops(L)-1 to 1 by -1 do
%p A340595     x:= 10^(1+ilog10(x))*L[i]+x
%p A340595   od;
%p A340595   x
%p A340595 end proc:
%p A340595 f:= proc(n) local F;
%p A340595   F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);
%p A340595   dcat(map(t -> t[1]$t[2], F)) mod n;
%p A340595 end proc:
%p A340595 g:= proc(n) option remember;
%p A340595      if isprime(n) then 0 else 1 + procname(f(n)) fi
%p A340595 end proc:
%p A340595 g(0):= 0: g(1):= 0:
%p A340595 V:= Array(0..30): count:= 0:
%p A340595 for n from 2 while count < 31 do
%p A340595   v:= f(n);
%p A340595   if v::integer and v <= 100 and V[v] = 0 then
%p A340595       count:= count+1; V[v]:= n;
%p A340595     fi
%p A340595 od:
%p A340595 convert(V,list);
%Y A340595 Cf. A340592, A340594.
%K A340595 nonn
%O A340595 0,1
%A A340595 _J. M. Bergot_ and _Robert Israel_, Jan 13 2021