%I #40 Nov 26 2020 23:41:39

%S 0,0,0,0,0,0,0,0,0,0,11,6,4,3,3,2,2,2,2,0,21,11,7,6,5,4,3,3,3,0,31,16,

%T 11,8,7,6,5,4,4,0,41,21,14,11,9,7,6,6,5,0,51,26,17,13,11,9,8,7,6,0,61,

%U 31,21,16,13,11,9,8,7,0,71,36,24,18,15,12,11,9

%N a(n) is the number of times it takes to iteratively subtract m from n where m is the largest nonzero proper suffix of n less than or equal to the remainder until no further subtraction is possible.

%C Subtraction terminates when the remainder is less than the smallest nonzero proper suffix of n. A suffix of n is n mod 10^k for some k and a proper suffix is one that is strictly less than n. Equivalently, a proper suffix of n is the decimal value of the digits of n with one or more leading digits removed.

%e a(131) = 11 since 131-31-31-31-31-1-1-1-1-1-1-1 = 0 has 11 subtractions;

%e a(132) = 6 since 132-32-32-32-32-2-2 = 0 has 6 subtractions;

%e a(133) = 4 since 133-33-33-33-33 = 1 has 4 subtractions.

%t count = 1000; SubCount = {};

%t Do[(n = m = k; c = 0;

%t While[n > 0,

%t If[n <= m, m = ToExpression[StringDrop[ToString[k], 1]], m];

%t If[m == Null || m == 0, Break[]]; n -= m;

%t If[n < 0, Break[]]; c++;

%t ]; AppendTo[SubCount, c];), {k, 1, count, 1}];

%t ListPlot[SubCount]

%t Print[SubCount];

%o (PARI) a(n)={my(m=n%(10^logint(n,10)), s=0); while(m>0, s+=n\m; n%=m; m%=10^logint(m,10)); s} \\ _Andrew Howroyd_, Nov 21 2020

%Y Cf. A217657.

%K nonn,base

%O 1,11

%A _Linus Jarbo_ and _Hugo Angulo_, Nov 15 2020