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A228893 Numbers n such that the concatenation of the frequency of each decimal digit of n is divisible by n. 0
1, 2, 4, 5, 10, 14, 20, 25, 32, 40, 50, 52, 73, 100, 112, 120, 125, 150, 152, 188, 200, 226, 240, 250, 300, 305, 320, 335, 400, 420, 500, 600, 674, 700, 1000, 1100, 1144, 1210, 1250, 1430, 2000, 2020, 2500, 2660, 3250, 4000, 4015, 5000, 5500, 6500, 8629, 10000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Start with any number n and denote(f0, f1,...,f9) the number of the digits 0, 1, 2,..., 9 of n. The sequence lists the numbers n such that m = f0f1f2f3f4f5f6f7f8f9/n is an integer.

The corresponding m are:

100000000, 5000000, 25000, 2000, 110000000, 7150000, 50500000, 400400, 343750, 25002500, 20000200, 192500, 13700, 21000000, 1875000, 9250000, 880080, 7333400, 723750, 531915,...

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

226 is in the sequence because the table of the frequencies is:

frequency of 0 = 0;

frequency of 1 = 0;

frequency of 2 = 2;

frequency of 3 = 0;

frequency of 4 = 0;

frequency of 5 = 0;

frequency of 6 = 1;

frequency of 7 = 0;

frequency of 8 = 0;

frequency of 9 = 0.

The concatenation of the frequencies is 20001000, and 20001000/226 = 88500.

MAPLE

with(numtheory): T:=array(0..9):

  for n from 1 to 200000 do:

     x:=convert(n, base, 10):n1:=nops(x):(1..n1):

       for k from 0 to 9 do:

          T[k]:=0:od:jj:=0:

            for i from 0 to 9 do:

              for j from 1 to n1 do:

                if x[j]=i

                then

                T[i]:=T[i]+1:jj:=jj+1:

                else

                fi:

              od:

            od:

               s:= sum('T[9-i]*10^i', 'i'=0..9):s1:=s/n:

               if floor(s1)=s1

               then

               printf(`%d, `, n):

               else

               fi:

       od:

CROSSREFS

Sequence in context: A002237 A329136 A067935 * A272622 A097133 A023165

Adjacent sequences:  A228890 A228891 A228892 * A228894 A228895 A228896

KEYWORD

nonn,base,less

AUTHOR

Michel Lagneau, Sep 07 2013

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)