A255893 Perfect squares k such that each decimal digit of k is equal to the difference of at least two other digits of k.

59049, 60516, 91809, 130321, 131044, 150544, 199809, 255025, 299209, 396900, 656100, 660969, 670761, 774400, 811801, 998001, 1018081, 1022121, 1089936, 1188100, 1212201, 1452025, 1585081, 1677025, 1697809, 1760929, 2047761, 2056356, 2064969, 2155024, 2205225

Offset

1,1

Comments

Let x(1)x(2)... x(q-1)x(q) denote the decimal expansion of a square k. The sequence lists the squares k such that, for each index i, x(i) = x(u) - x(v) for some indices u and v. Each term of the sequence contains at least two identical decimal digits and at least one 0 digit.

Subsequence of A255966.

The number 10948273956 is the smallest square of the sequence containing 10 distinct digits.

Links

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

Example

59049 is in the sequence because:
5 = 9 - 4;
9 = 9 - 0;
0 = 9 - 9;
4 = 9 - 5;
9 = 9 - 0.

Maple

with(numtheory):
for m from 10 to 10000 do:
   n:=m^2: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:

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n, lng = 1 + Floor@ Log10@ n}, Union@ Table[c = Complement[ Range@ lng, {i}]; MemberQ[ Union@ Flatten@ Table[Abs[id[[j]] - id[[k]]], {j, c}, {k, c}], id[[i]]], {i, lng}] == {True}]; Select[ Range@ 1450^2, fQ] (* Robert G. Wilson v, Mar 10 2015 *)

Crossrefs

Cf. A255892, A255893, A255917, A255966.

Sequence in context: A321826 A176763 A176769 * A046323 A368950 A017081

Adjacent sequences: A255890 A255891 A255892 * A255894 A255895 A255896

Keyword

nonn,base

Author

Michel Lagneau, Mar 09 2015

Status

approved