OFFSET
0,1
COMMENTS
a(n) is the least k >= 2 from which it takes exactly n iterations of A340592 to reach 0, 1 or a prime.
EXAMPLE
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.
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 13 2021
STATUS
approved