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A255966 Number n such that each decimal digit of n is equal to the difference of at least two other digits of n. 4
101, 110, 202, 220, 303, 330, 404, 440, 505, 550, 606, 660, 707, 770, 808, 880, 909, 990, 1001, 1010, 1011, 1100, 1101, 1110, 2002, 2020, 2022, 2200, 2202, 2220, 3003, 3030, 3033, 3300, 3303, 3330, 4004, 4040, 4044, 4400, 4404, 4440, 5005, 5050, 5055, 5500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let x(1)x(2)... x(q-1)x(q) denote the decimal expansion of a number n. The sequence lists the numbers n such that, for all index i, x(i) = x(j) - x(k) for some index j and k.

The sequence is infinite because a(n)*10^m for all integer m is also in the sequence.

All number of the sequence contains at least two identical decimal digit. a(n) contains at least a decimal digit equals to zero. The number

12345678909 is the smallest element of the sequence containing 10 distinct digits.

The prime numbers of the sequence are 101, 10111, 10133, 10177,...

The squares of the sequence are  59049, 60516, 91809, 130321,...

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..10000

EXAMPLE

34707 is in the sequence because 3=7-4, 4=7-3,7=7-0 and 0=7-7.

MAPLE

with(numtheory):

for n from 100 to 10000 do:

  x:=convert(n, base, 10):n1:=nops(x):c:=0:T:=array(1..n1-1):

    for nn from 1 to n1 do:

     z:=x[nn]:

     k:=0:

      for j from 1 to n1 do:

       if nn<>j

       then

       k:=k+1:T[k]:=x[j]:

       else

       fi:

      od:

      ii:=0:

        for a from 1 to n1-1 while(ii=0) do:

         for b from a+1 to n1-1 while(ii=0) do:

         if z=abs(T[a]-T[b]) then ii:=1:c:=c+1:

         else

         fi:

        od:od:

      od:

      if c=n1 then printf(`%d, `, n):

      else

      fi:

  od:

CROSSREFS

Cf. A255892, A255893, A255917.

Sequence in context: A025349 A025341 A290725 * A305396 A266717 A303571

Adjacent sequences:  A255963 A255964 A255965 * A255967 A255968 A255969

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Mar 12 2015

STATUS

approved

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Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)