A363373 - OEIS

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

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OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..27.

EXAMPLE

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.

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;