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 A018885 Squares using no more than two distinct digits. 7
 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 *) Select[Range[0, 100000]^2, Count[DigitCount[#], 0]>7&] (* Harvey P. Dale, Jul 25 2020 *) 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: A305559 A221222 A144913 * A025741 A179459 A325148 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 August 9 16:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)