A123912 Numbers whose square starts with 2 identical digits.

15, 21, 34, 47, 58, 67, 88, 94, 105, 106, 107, 108, 109, 149, 150, 151, 182, 183, 184, 210, 211, 212, 235, 236, 257, 258, 278, 279, 297, 298, 315, 316, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 470, 471, 472, 473, 474, 475, 476

Offset: 1

Author

Tanya Khovanova, Oct 28 2006

Keywords

• base
• nonn

Examples

			15^2 = 225.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Maple

q:= n-> (s-> is(s[1]=s[2]))(""||(n^2)):
select(q, [$4..1000])[];  # Alois P. Heinz, Apr 22 2022

Mathematica

idf[k_]:=IntegerDigits[k^2];Select[Range[4,476],idf[#][[1]]==idf[#][[2]]&] (* Or,to explore member numbers for a range of squares, adjust n2 as needed *) s={};Do[If[IntegerQ[Sqrt[n2]],AppendTo[s,Sqrt[n2]]],{n2,110000,119999}];s (* James C. McMahon, Nov 24 2024 *)

PARI

isok(k) = my(d=digits(k^2)); (#d>=2) && (d[1]==d[2]); \\ Michel Marcus, Nov 27 2024