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
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
0 inserted and definition edited by Jon E. Schoenfield, Jan 15 2014
STATUS
approved