

A204502


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


20



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

1,3


COMMENTS

Or, numbers n such that n^2, with its last base9 digit dropped, is again a square. (Except maybe for the 3 initial terms whose square has only 1 digit in base 9.)


LINKS

Table of n, a(n) for n=1..63.
M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
Index to sequences related to truncating digits of squares.


FORMULA

Conjecture: a(n) = 3*n12 for n>5. G.f.: x^2*(x^2+x+1)*(x^3x+1)/(x1)^2. [Colin Barker, Nov 23 2012]


MATHEMATICA

Select[Range[0, 200], IntegerQ[Sqrt[Floor[#^2/9]]]&] (* Harvey P. Dale, May 05 2018 *)


PROG

(PARI) b=9; for(n=0, 200, issquare(n^2\b) & print1(n", "))


CROSSREFS

The squares are in A204503, the squares with last base9 digit dropped in A204504, and the square roots of the latter in A028310.
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).
Sequence in context: A128166 A240470 A112249 * A062437 A060729 A229169
Adjacent sequences: A204499 A204500 A204501 * A204503 A204504 A204505


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 15 2012


STATUS

approved



