cp's OEIS Frontend

A323076 Number of iterations of map x -> 1+(x-(largest divisor d < x)), starting from x=n, needed to reach a fixed point, which is always either a prime or 1.

%I A323076 #11 Jan 04 2019 17:37:36
%S A323076 0,0,0,1,0,2,0,1,1,3,0,1,0,2,1,2,0,4,0,1,2,2,0,1,3,3,1,2,0,3,0,1,1,5,
%T A323076 1,1,0,2,2,3,0,3,0,1,1,2,0,4,1,4,2,2,0,3,2,1,3,4,0,1,0,2,1,2,1,6,0,2,
%U A323076 1,2,0,1,0,3,3,3,1,4,0,1,3,4,0,1,2,2,1,2,0,3,1,1,2,5,2,2,0,5,1,3,0,3,0,1,1
%N A323076 Number of iterations of map x -> 1+(x-(largest divisor d < x)), starting from x=n, needed to reach a fixed point, which is always either a prime or 1.
%C A323076 Differs from A064918 at n = 25, 48, 51, 69, 75, 81, 85, 94, 95, 99, 100, 111, 115, 121, ...
%H A323076 Antti Karttunen, <a href="/A323076/b323076.txt">Table of n, a(n) for n = 1..20669</a>
%H A323076 Antti Karttunen, <a href="/A323076/a323076.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A323076 If n == (1+A060681(n)), then a(n) = 0, otherwise a(n) = 1 + a(1+A060681(n)).
%t A323076 {0}~Join~Array[-2 + Length@ NestWhileList[1 + (# - Divisors[#][[-2]]) &, #, UnsameQ, All] &, 104, 2] (* _Michael De Vlieger_, Jan 04 2019 *)
%o A323076 (PARI)
%o A323076 A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
%o A323076 A323076(n) = { my(nn = 1+A060681(n)); if(nn==n,0,1+A323076(nn)); };
%Y A323076 Cf. A060681, A064918, A323075 (the fixed points reached), A323077, A323079.
%Y A323076 Cf. also A039651.
%K A323076 nonn
%O A323076 1,6
%A A323076 _Antti Karttunen_, Jan 04 2019