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A340594
a(n) is the number of iterations of A340592 starting from n, until 0, 1 or a prime is reached.
3
0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 3, 1, 0, 2, 1, 1, 3, 1, 0, 2, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 0, 4, 0, 1, 2, 2, 0, 1, 2, 1, 1, 1, 0, 1, 3, 1, 2, 4, 0, 2, 0, 3, 2, 2, 5, 1, 0, 1, 1, 1, 0, 3, 0, 2, 4, 2, 2, 2, 0, 6, 2, 3, 0, 1, 1, 1, 2, 3, 0, 2, 3, 2, 2, 1, 2, 1, 0, 3, 2
OFFSET
2,7
COMMENTS
a(n) = 0 if n is prime.
LINKS
FORMULA
a(n) = A066247(n)*(1 + a(A340592(n))).
EXAMPLE
A340592(21) = 16, A340592(16) = 14, A340592(14) = 13 is prime, so a(21) = 3.
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:
map(g, [$1..1000]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 13 2021
STATUS
approved