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

2, 4, 8, 21, 42, 65, 80, 217, 488, 721, 2120, 2349, 2796, 9214, 16043, 23287, 28626, 43588, 58176, 116982, 213435, 444329, 640673, 967248, 1399895, 1449156, 1528785, 2768054, 2915135, 3631071, 3673118, 5032731, 12977420

Offset: 0

Author

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

Keywords

• nonn

Comments

a(n) is the least k >= 2 from which it takes exactly n iterations of A340592 to reach 0, 1 or a prime.

Examples

			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.
		

Crossrefs

Cf. A340592, A340594.

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:
V:= Array(0..30): count:= 0:
for n from 2 while count < 31 do
  v:= f(n);
  if v::integer and v <= 100 and V[v] = 0 then
      count:= count+1; V[v]:= n;
    fi
od:
convert(V,list);