A354760 a(0) = 0; for n >= 1, a(n) = a(n - A054055(n)) + 1.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13

Offset: 0

Author

Ctibor O. Zizka, Jun 06 2022

Keywords

• base
• easy
• nonn

Comments

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k by k - A054055(k). a(n) ~ n/ln(n).

Examples

			n = 12, a(12) = 1 + a(12 - A054055(12)) = 1 + a(10) = 1 + 1 + a(10 - A054055(10)) = 2 + a(9) = 2 + 1 + a(9 - A054055(9)) = 2 + 1 + 0 = 3.
		

Crossrefs

Cf. A054055.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = a[n - Max[IntegerDigits[n]]] + 1; Array[a, 100, 0] (* Amiram Eldar, Jun 06 2022 *)