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A338920
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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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0
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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
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OFFSET
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1,11
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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