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

1,1

Links

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

Example

15^2 = 225.

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 *)

Prog

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

Crossrefs

Sequence in context: A168354 A190358 A090999 * A346812 A296244 A309005

Adjacent sequences: A123909 A123910 A123911 * A123913 A123914 A123915

Keyword

base,nonn

Author

Tanya Khovanova, Oct 28 2006

Status

approved