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A018885 Squares using no more than two distinct digits. 5
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 225, 400, 441, 484, 676, 900, 1444, 7744, 10000, 11881, 29929, 40000, 44944, 55225, 69696, 90000, 1000000, 4000000, 9000000, 9696996, 100000000, 400000000, 900000000, 6661661161, 10000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Is 6661661161 the largest term not of the form 10^k, 4*10^k or 9*10^k? Any larger ones must have >= 22 digits. - Robert Israel, Dec 03 2015

LINKS

Shawn A. Broyles, Table of n, a(n) for n = 1..85

Alexandru Gica and Laurentiu Panaitopol, On Oblath's Problem, J. Integer Seqs., Vol. 6(3), 2003, article 03.3.5.

Eric Weisstein's World of Mathematics, Square Number

FORMULA

For n > 4, a(n) = A016069(n-4)^2.

MAPLE

F:= proc(r, a, b, m)

# get all squares starting with r, with at most m further digits, all from {a, b} where a < b

local res, Ls, Us, L, U, looking;

if issqr(r) then res:= r else res:= NULL fi;

if m = 0 then return res fi;

Ls:= r*10^m + a*(10^m-1)/9;

Us:= r*10^m + b*(10^m-1)/9;

L:= isqrt(Ls);

if L^2 > Ls then L:= L-1 fi;

U:= isqrt(Us);

if U^2 < Us then U:= U+1 fi;

if L > U then res

else res, procname(10*r+a, a, b, m-1), procname(10*r+b, a, b, m-1)

fi

end proc:

S2:= {seq(i^2 mod 100, i=0..99)}:

prs:= map(t -> `if`(t < 10, {0, t}, {(t mod 10), (t - (t mod 10))/10}), S2):

prs:= map(p -> `if`(nops(p)=1, seq(p union {s}, s={$0..9} minus p), p), prs):

Res:= NULL:

for p in prs do

  a:= min(p); b:= max(p);

  if a > 0 then

     Res:= Res, F(a, a, b, 14);

  fi;

  Res:= Res, F(b, a, b, 14);

od:

sort(convert({0, Res}, list)); # Robert Israel, Dec 03 2015

MATHEMATICA

Select[Range[0, 10^5]^2, Length@ Union@ IntegerDigits@ # <= 2 &] (* Michael De Vlieger, Dec 03 2015 *)

PROG

(PARI) for (n=0, 10^6, if ( #Set(digits(n^2))<=2, print1(n^2, ", ") ) ); \\ Michel Marcus, May 21 2015

CROSSREFS

Cf. A016069, A016070, A018884.

Sequence in context: A253909 A221222 A144913 * A025741 A179459 A030476

Adjacent sequences:  A018882 A018883 A018884 * A018886 A018887 A018888

KEYWORD

nonn,base

AUTHOR

David W. Wilson

EXTENSIONS

0 inserted and definition edited by Jon E. Schoenfield, Jan 15 2014

STATUS

approved

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Last modified January 17 09:45 EST 2018. Contains 297815 sequences.