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%I #42 Mar 08 2021 02:47:35
%S 2,5,8,11,14,17,18,20,23,26,29,32,35,38,41,44,45,47,50,53,56,59,62,65,
%T 68,71,72,74,77,80,83,86,89,92,95,98,99,101,104,107,110,113,116,119,
%U 122,125,126,128,131,134,137,140,143,146,149,152,153,155
%N Numbers of the form 9^i*(3*j+2).
%C The numbers not of the form x^2+3y^2+3z^2.
%C Numbers whose squarefree part is congruent to 2 modulo 3. - _Peter Munn_, May 17 2020
%C The asymptotic density of this sequence is 3/8. - _Amiram Eldar_, Mar 08 2021
%H Reinhard Zumkeller, <a href="/A055048/b055048.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 a(n) = A055040(n)/3. - _Peter Munn_, May 17 2020
%t max = 200; Select[ Union[ Flatten[ Table[ 9^i*(3*j + 2), {i, 0, Ceiling[Log[max]/Log[9]]}, {j, 0, Ceiling[( max/9^i - 2)/3]}]]], # <= max &] (* _Jean-François Alcover_, Oct 13 2011 *)
%o (Haskell)
%o a055048 n = a055048_list !! (n-1)
%o a055048_list = filter (s 0) [1..] where
%o s t u | m > 0 = even t && m == 2
%o | m == 0 = s (t + 1) u' where (u',m) = divMod u 3
%o -- _Reinhard Zumkeller_, Apr 07 2012
%o (PARI) is(n)=n/=9^valuation(n, 9); n%3==2 \\ _Charles R Greathouse IV_ and _V. Raman_, Dec 19 2013
%Y Intersection of A007417 and A189716.
%Y Complement of A055047 with respect to A007417.
%Y Complement of A055041 with respect to A189716.
%Y Cf. A007913, A055040.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jun 01 2000
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