This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354760 #12 Jun 06 2022 11:21:58 %S A354760 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, %T A354760 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, %U A354760 12,12,12,12,12,12,12,12,13,13,13,13,13,13,13 %N A354760 a(0) = 0; for n >= 1, a(n) = a(n - A054055(n)) + 1. %C A354760 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). %e A354760 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. %t A354760 a[0] = 0; a[n_] := a[n] = a[n - Max[IntegerDigits[n]]] + 1; Array[a, 100, 0] (* _Amiram Eldar_, Jun 06 2022 *) %Y A354760 Cf. A054055. %K A354760 base,easy,nonn %O A354760 0,11 %A A354760 _Ctibor O. Zizka_, Jun 06 2022