A067225 Numbers k such that k is a square and remains a square when its leading digit is increased by one.

576, 2025, 11025, 57600, 202500, 342225, 950625, 1102500, 3515625, 5760000, 9272025, 11390625, 20250000, 34222500, 95062500, 110250000, 196700625, 351562500, 576000000, 927202500, 1139062500, 2025000000, 3422250000, 5613755625, 5909765625, 9506250000, 11025000000, 19670062500

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

576 = 24^2 and 676 = 26^2, so 576 is a term of the sequence.

Maple

for n from 1 to 10^6 do if issqr(n^2+10^(length(n^2)-1)) then printf(`%d, `, n^2); fi:od:

Mathematica

f[n_] := Block[{a = IntegerDigits[n]}, a[[1]] = a[[1]] + 1; FromDigits[a]]; Select[ Range[10^5], IntegerQ[ Sqrt[ f[ #^2]]] & ]^2
Select[Range[60000]^2, IntegerQ[Sqrt[#+10^(IntegerLength[#]-1)]]&] (* Harvey P. Dale, May 27 2014 *)

Crossrefs

Sequence in context: A189990 A064254 A281242 * A325475 A268797 A390120

Adjacent sequences: A067222 A067223 A067224 * A067226 A067227 A067228

Keyword

base,nonn

Author

Joseph L. Pe, Feb 20 2002

Extensions

Edited and extended by Robert G. Wilson v, Feb 21 2002

More terms from David A. Corneth, Jun 07 2025

Status

approved