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A055048
Numbers of the form 9^i*(3*j+2).
7
2, 5, 8, 11, 14, 17, 18, 20, 23, 26, 29, 32, 35, 38, 41, 44, 45, 47, 50, 53, 56, 59, 62, 65, 68, 71, 72, 74, 77, 80, 83, 86, 89, 92, 95, 98, 99, 101, 104, 107, 110, 113, 116, 119, 122, 125, 126, 128, 131, 134, 137, 140, 143, 146, 149, 152, 153, 155
OFFSET
1,1
COMMENTS
The numbers not of the form x^2+3y^2+3z^2.
Numbers whose squarefree part is congruent to 2 modulo 3. - Peter Munn, May 17 2020
The asymptotic density of this sequence is 3/8. - Amiram Eldar, Mar 08 2021
LINKS
L. J. Mordell, A new Waring's problem with squares of linear forms, Quart. J. Math., 1 (1930), 276-288 (see p. 283).
FORMULA
a(n) = A055040(n)/3. - Peter Munn, May 17 2020
MATHEMATICA
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 *)
PROG
(Haskell)
a055048 n = a055048_list !! (n-1)
a055048_list = filter (s 0) [1..] where
s t u | m > 0 = even t && m == 2
| m == 0 = s (t + 1) u' where (u', m) = divMod u 3
-- Reinhard Zumkeller, Apr 07 2012
(PARI) is(n)=n/=9^valuation(n, 9); n%3==2 \\ Charles R Greathouse IV and V. Raman, Dec 19 2013
CROSSREFS
Intersection of A007417 and A189716.
Complement of A055047 with respect to A007417.
Complement of A055041 with respect to A189716.
Sequence in context: A356057 A189525 A189369 * A045930 A140099 A276385
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 01 2000
STATUS
approved