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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Example: 2357^2 = 5555449.

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]<q, k++ ]; Take[s, q]
(* Hans Havermann, Aug 30 2007 *)

Prog

(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

Crossrefs

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

Sequence in context: A251295 A220626 A136420 * A346940 A134966 A108419

Adjacent sequences: A132388 A132389 A132390 * A132392 A132393 A132394

Keyword

nonn,base,look

Author

Jonathan Vos Post, Aug 29 2007

Status

approved