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A204503 Squares n^2 such that floor(n^2/9) is again a square. 20


%S 0,1,4,9,16,36,81,144,225,324,441,576,729,900,1089,1296,1521,1764,

%T 2025,2304,2601,2916,3249,3600,3969,4356,4761,5184,5625,6084,6561,

%U 7056,7569,8100,8649,9216,9801,10404,11025,11664,12321,12996,13689,14400,15129,15876

%N Squares n^2 such that floor(n^2/9) is again a square.

%C Or: Squares which remain squares when their last base-9 digit is dropped.

%C (For the first three terms, which have only 1 digit in base 9, dropping that digit is meant to yield zero.)

%C Base-9 analog of A055792 (base 2), A055793 (base 3), A055808 (base 4), A055812 (base 5), A055851 (base 6), A055859 (base 7), A055872(base 8) and A023110 (base 10).

%H M. F. Hasler, <a href="/wiki/M._F._Hasler/Truncated_squares">Truncated squares</a>, OEIS wiki, Jan 16 2012

%H <a href="/index/Sq#sqtrunc">Index to sequences related to truncating digits of squares</a>.

%F a(n) = A204502(n)^2.

%F Conjectures: a(n) = 9*(n-4)^2 for n>5. G.f.: x^2*(7*x^6-12*x^5-11*x^4-x-1) / (x-1)^3. - _Colin Barker_, Sep 15 2014

%t Select[Range[0,200]^2,IntegerQ[Sqrt[Floor[#/9]]]&] (* _Harvey P. Dale_, Jan 27 2012 *)

%o (PARI) b=9;for(n=1,200,issquare(n^2\b) & print1(n^2,","))

%K nonn,base

%O 1,3

%A _M. F. Hasler_, Jan 15 2012

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Last modified April 13 07:51 EDT 2021. Contains 342935 sequences. (Running on oeis4.)