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A204502 Numbers such that floor[a(n)^2 / 9] is a square.

%I A204502 #20 May 05 2018 12:43:00
%S A204502 0,1,2,3,4,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,
%T A204502 66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,
%U A204502 126,129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177
%N A204502 Numbers such that floor[a(n)^2 / 9] is a square.
%C A204502 Or, numbers n such that n^2, with its last base-9 digit dropped, is again a square. (Except maybe for the 3 initial terms whose square has only 1 digit in base 9.)
%H A204502 M. F. Hasler, <a href="/wiki/M. F. Hasler/Truncated_squares">Truncated squares</a>, OEIS wiki, Jan 16 2012
%H A204502 <a href="/index/Sq#sqtrunc">Index to sequences related to truncating digits of squares</a>.
%F A204502 Conjecture: a(n) = 3*n-12 for n>5. G.f.: x^2*(x^2+x+1)*(x^3-x+1)/(x-1)^2. [_Colin Barker_, Nov 23 2012]
%t A204502 Select[Range[0,200],IntegerQ[Sqrt[Floor[#^2/9]]]&] (* _Harvey P. Dale_, May 05 2018 *)
%o A204502 (PARI) b=9;for(n=0,200,issquare(n^2\b) & print1(n","))
%Y A204502 The squares are in A204503, the squares with last base-9 digit dropped in A204504, and the square roots of the latter in A028310.
%Y A204502 Cf. A031149=sqrt(A023110) (base 10), A204514=sqrt(A055872) (base 8), A204516=sqrt(A055859) (base 7), A204518=sqrt(A055851) (base 6), A204520=sqrt(A055812) (base 5), A004275=sqrt(A055808) (base 4), A001075=sqrt(A055793) (base 3), A001541=sqrt(A055792) (base 2).
%K A204502 nonn
%O A204502 1,3
%A A204502 _M. F. Hasler_, Jan 15 2012