A338920 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.

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

Offset

1,11

Comments

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.

Links

Table of n, a(n) for n=1..78.

Example

a(131) = 11 since 131-31-31-31-31-1-1-1-1-1-1-1 = 0 has 11 subtractions;
a(132) = 6 since 132-32-32-32-32-2-2 = 0 has 6 subtractions;
a(133) = 4 since 133-33-33-33-33 = 1 has 4 subtractions.

Mathematica

count = 1000; SubCount = {};
Do[(n = m = k; c = 0;
   While[n > 0,
    If[n <= m, m = ToExpression[StringDrop[ToString[k], 1]], m];
    If[m == Null || m == 0, Break[]]; n -= m;
    If[n < 0, Break[]]; c++;
    ]; AppendTo[SubCount, c]; ), {k, 1, count, 1}];
ListPlot[SubCount]
Print[SubCount];

Prog

(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

Crossrefs

Cf. A217657.

Sequence in context: A288069 A236175 A193813 * A080501 A122098 A347518

Adjacent sequences: A338917 A338918 A338919 * A338921 A338922 A338923

Keyword

nonn,base

Author

Linus Jarbo and Hugo Angulo, Nov 15 2020

Status

approved