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.

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, 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, 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

Offset

1,6

Comments

Differs from A064918 at n = 25, 48, 51, 69, 75, 81, 85, 94, 95, 99, 100, 111, 115, 121, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..20669

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

If n == (1+A060681(n)), then a(n) = 0, otherwise a(n) = 1 + a(1+A060681(n)).

Mathematica

{0}~Join~Array[-2 + Length@ NestWhileList[1 + (# - Divisors[#][[-2]]) &, #, UnsameQ, All] &, 104, 2] (* Michael De Vlieger, Jan 04 2019 *)

Prog

(PARI)
A060681(n) = (n-if(1==n, n, n/vecmin(factor(n)[, 1])));
A323076(n) = { my(nn = 1+A060681(n)); if(nn==n, 0, 1+A323076(nn)); };

Crossrefs

Cf. A060681, A064918, A323075 (the fixed points reached), A323077, A323079.

Cf. also A039651.

Sequence in context: A326728 A330944 A064918 * A286471 A176079 A067586

Adjacent sequences: A323073 A323074 A323075 * A323077 A323078 A323079

Keyword

nonn

Author

Antti Karttunen, Jan 04 2019

Status

approved