A363373 a(n) is the least k such that, if x_0, x_1, x_2, ... are the iterations of the arithmetic derivative A003415 starting with x_0 = k, x_0 > x_1 > ... > x_n.

0, 1, 2, 6, 9, 14, 33, 62, 177, 886, 1155, 1719, 3255, 4018, 13377, 19942, 46022, 103401, 193426, 422751, 634113, 1080742, 2850591, 5493662, 10252635, 25631525, 51217666, 135055839

Offset: 0

Author

Robert Israel, May 29 2023

Keywords

• nonn
• more

Comments

a(n) is the least k such that the first n iterations of A003415 starting at k are decreasing.

a(n) is the least k such that A361869(k) = n.

Examples

			a(3) = 6 because the iterations of A003415 starting at 6 are 6 > 5 > 1 > 0 = 0.
First differs from A189760 and A327967 at 9, where a(9) = 886 (corresponding to iterations 886 > 445 > 94 > 49 > 14 > 9 > 6 > 5 > 1 > 0) while A189760(9) = A327967(9) = 414 < A003415(414) = 501.
		

Crossrefs

Cf. A003415, A189760, A327967, A361869.

Programs

Maple

ader:= proc(n) local t;
  n * add(t[2]/t[1], t = ifactors(n)[2])
end proc:
f:= proc(n) option remember; local t;
   t:= ader(n);
   if t < n then procname(t)+1 else 0 fi
end proc:
M:= 25: V:= Array(0..M,-1): count:= 0:
for n from 0 while count <= M do
  v:= f(n);
  if V[v] = -1 then count:= count+1; V[v]:= n fi;
od:
convert(V,list);