A255966 Numbers n such that each decimal digit of n is equal to the difference of at least two other digits of n.

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

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 integers m is also in the sequence.

All numbers of the sequence contain at least two identical decimal digits. a(n) contains at least one decimal digit equal 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

Extensions

Comments corrected by Harvey P. Dale, Oct 17 2021

Status

approved