login
A067225
Numbers n such that n is a square and remains a square when its leading digit is increased by one.
0
576, 2025, 11025, 57600, 202500, 342225, 950625, 1102500, 3515625, 5760000, 9272025, 11390625, 20250000, 34222500, 95062500, 110250000, 196700625, 351562500, 576000000, 927202500, 1139062500, 2025000000, 3422250000
OFFSET
1,1
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 A036514
KEYWORD
base,nonn
AUTHOR
Joseph L. Pe, Feb 20 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Feb 21 2002
STATUS
approved