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A132391 Numbers whose square starts with 4 identical digits. 2

%I

%S 2357,2582,3334,4714,5774,6667,8165,8819,9428,10541,10542,10543,10544,

%T 10545,14907,14908,14909,18257,18258,18259,21081,21082,21083,23570,

%U 23571,25819,25820,27888,27889,29813,29814,31622,33332,33333

%N Numbers whose square starts with 4 identical digits.

%e Example: 2357^2 = 5555449.

%t Select[Range[10, 50000], Length[Union[Take[IntegerDigits[ #^2], 4]]] == 1 & ]

%t Comment from _Hans Havermann_, Aug 30 2007: Here's a more generic Mathematica program that calculates the first q terms of squares starting with n identical digits:

%t n=4; q=30; t=Table[(10^n-1)*i/9, {i,1,9}]; u=Sqrt[Union[t,10*t]];

%t v=Sqrt[Union[t+1, 10*(t+1)]]; k=1; While[s=Sort[Flatten[Table[Union

%t [Table[Range[Ceiling[10^j*u[[i]]], f=10^j*v[[i]]; If[IntegerQ[f],

%t f=f-1]; Floor[f]], {i,1,18}]], {j,0,k}]]]; Length[s]<q, k++ ]; Take[s,q]

%Y Cf. A119887, A119511, A131573, A119866, A133183.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Aug 29 2007

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Last modified February 25 08:48 EST 2020. Contains 332221 sequences. (Running on oeis4.)