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A255893 Perfect squares k such that each decimal digit of k is equal to the difference of at least two other digits of k. 4
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 (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 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: A235953 A343374 A321826 * A046323 A017081 A017165

Adjacent sequences:  A255890 A255891 A255892 * A255894 A255895 A255896

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Mar 09 2015

STATUS

approved

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Last modified January 28 20:33 EST 2022. Contains 350662 sequences. (Running on oeis4.)