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%I #25 Mar 08 2021 02:46:55
%S 6,15,24,33,42,51,54,60,69,78,87,96,105,114,123,132,135,141,150,159,
%T 168,177,186,195,204,213,216,222,231,240,249,258,267,276,285,294,297,
%U 303,312,321,330,339,348,357,366,375,378,384,393,402,411
%N Numbers of the form 3^(2i+1)*(3*j+2).
%C Numbers not of the form x^2+y^2+3z^2.
%C Numbers whose squarefree part is congruent to 6 modulo 9. - _Peter Munn_, May 17 2020
%C The asymptotic density of this sequence is 1/8. - _Amiram Eldar_, Mar 08 2021
%H Reinhard Zumkeller, <a href="/A055040/b055040.txt">Table of n, a(n) for n = 1..10000</a>
%H L. J. Mordell, <a href="https://doi.org/10.1093/qmath/os-1.1.276">A new Waring's problem with squares of linear forms</a>, Quart. J. Math., 1 (1930), 276-288 (see p. 283).
%F G.f.: [x(x+2)(x^2+x+1)(x^7+x^3+1)]/(x^11-x^10-x+1) (conjectured).
%t max = 500; Select[ Union[ Flatten[ Table[3^(2*i + 1)*(3*j + 2), {i, 0, Ceiling[ Log[max/6]/Log[9]]}, {j, 0, Ceiling[(max/9^i - 6)/9]}]]], # <= max &] (* _Jean-François Alcover_, Oct 13 2011 *)
%o (Haskell)
%o a055040 n = a055040_list !! (n-1)
%o a055040_list = map (* 3) a055048_list
%o -- _Reinhard Zumkeller_, Apr 07 2012
%Y Equals 3*A055048(n).
%Y Intersection of A145204 and A189715.
%Y Complement of A055041 with respect to A145204\{0}.
%Y Complement of A055047 with respect to A189715.
%Y Cf. A007913.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_, Jun 01 2000
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