A355300 a(0) = 0; for n >= 1, a(n) = a(A007088(n) mod n) + 1.

0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 2, 2, 1, 3, 2, 4, 1, 1, 3, 3, 2, 2, 3, 4, 3, 4, 2, 4, 1, 3, 2, 2, 2, 2, 3, 3, 1, 3, 1, 2, 2, 5, 2, 3, 2, 6, 2, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 2, 3, 2, 1, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 4, 4, 1, 3, 2, 4, 1, 3, 2, 4, 3, 3, 2, 2, 2

Offset: 0

Author

Ctibor O. Zizka, Jun 27 2022

Keywords

• nonn
• base

Comments

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k by A007088(k) mod k. For a(n) = 1 see A032533.

a(95980631) = 26. - Charles R Greathouse IV, Jun 30 2022

Examples

			n = 12, a(12) = a(1100 mod 12) + 1 = a(8) + 1 = a(1000 mod 8) + 2 = a(0) + 2 = 2.
		

Crossrefs

Cf. A007088, A032533.

Programs

Mathematica

a[n_] := a[n] = a[Mod[FromDigits[IntegerDigits[n, 2]], n]] + 1; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Jun 27 2022 *)

PARI

f(n) = fromdigits(binary(n), 10); \\ A007088
a(n) = if (n, a(f(n) % n)+1, 0); \\ Michel Marcus, Jun 27 2022