A132391 Numbers whose square starts with 4 identical digits.
2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10541, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333
Offset: 1
Examples
Example: 2357^2 = 5555449.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
R:= NULL: count:= 0: for d from 1 while count < 100 do for i from 1 to 9 do L:= i*1111*10^d; X:= [$ceil(sqrt(L)) .. floor(sqrt(L+10^d-1))]; m:= nops(X); if m > 0 then count:= count+nops(X); R:= R, op(X); fi od od: R; # Robert Israel, Mar 12 2021 -
Mathematica
Select[Range[10, 50000], Length[Union[Take[IntegerDigits[ #^2], 4]]] == 1 & ] (* or *) (* Here's a more generic Mathematica program that calculates the first q terms of squares starting with n identical digits *) n=4; q=30; t=Table[(10^n-1)*i/9, {i,1,9}]; u=Sqrt[Union[t,10*t]]; v=Sqrt[Union[t+1, 10*(t+1)]]; k=1; While[s=Sort[Flatten[Table[Union [Table[Range[Ceiling[10^j*u[[i]]], f=10^j*v[[i]]; If[IntegerQ[f], f=f-1]; Floor[f]], {i,1,18}]], {j,0,k}]]]; Length[s] -
Python
def aupto(limit): alst = [] for m in range(34, limit+1): if len(set(str(m*m)[:4])) == 1: alst.append(m) return alst print(aupto(33333)) # Michael S. Branicky, Mar 12 2021