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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
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
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Mar 09 2015
STATUS
approved