Linus Jarbo - cp's OEIS frontend

User: Linus Jarbo

Linus Jarbo has authored 1 sequences.

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

Linus Jarbo and Hugo Angulo, Nov 15 2020

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.

			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.

Cf. A217657.

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];

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

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User: Linus Jarbo

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.

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