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A204502
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Numbers such that floor[a(n)^2 / 9] is a square.
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20
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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, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177
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OFFSET
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1,3
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COMMENTS
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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.)
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LINKS
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FORMULA
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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]
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MATHEMATICA
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Select[Range[0, 200], IntegerQ[Sqrt[Floor[#^2/9]]]&] (* Harvey P. Dale, May 05 2018 *)
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PROG
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(PARI) b=9; for(n=0, 200, issquare(n^2\b) & print1(n", "))
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CROSSREFS
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The squares are in A204503, the squares with last base-9 digit dropped in A204504, and the square roots of the latter in A028310.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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