%I #5 Jan 14 2021 02:48:03
%S 2,4,8,21,42,65,80,217,488,721,2120,2349,2796,9214,16043,23287,28626,
%T 43588,58176,116982,213435,444329,640673,967248,1399895,1449156,
%U 1528785,2768054,2915135,3631071,3673118,5032731,12977420
%N a(n) is the least k for which A340594(k) = n.
%C a(n) is the least k >= 2 from which it takes exactly n iterations of A340592 to reach 0, 1 or a prime.
%e 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 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 V:= Array(0..30): count:= 0:
%p for n from 2 while count < 31 do
%p v:= f(n);
%p if v::integer and v <= 100 and V[v] = 0 then
%p count:= count+1; V[v]:= n;
%p fi
%p od:
%p convert(V,list);
%Y Cf. A340592, A340594.
%K nonn
%O 0,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 13 2021