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Numbers n such that n is a square and remains a square when its leading digit is increased by one.
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%I #7 May 27 2014 15:11:18

%S 576,2025,11025,57600,202500,342225,950625,1102500,3515625,5760000,

%T 9272025,11390625,20250000,34222500,95062500,110250000,196700625,

%U 351562500,576000000,927202500,1139062500,2025000000,3422250000

%N Numbers n such that n is a square and remains a square when its leading digit is increased by one.

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

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

%t f[n_] := Block[{a = IntegerDigits[n]}, a[[1]] = a[[1]] + 1; FromDigits[a]]; Select[ Range[10^5], IntegerQ[ Sqrt[ f[ #^2]]] & ]^2

%t Select[Range[60000]^2,IntegerQ[Sqrt[#+10^(IntegerLength[#]-1)]]&] (* _Harvey P. Dale_, May 27 2014 *)

%K base,nonn

%O 1,1

%A _Joseph L. Pe_, Feb 20 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 21 2002