%I A008585
%S A008585 0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,
%T A008585 57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,
%U A008585 108,111,114,117,120,123,126,129,132,135,138,141,144
%N A008585 a(n) = 3*n.
%C A008585 If n != 1 and n^2+2 is prime then n is a member of this sequence. - Cino 
               Hilliard (hillcino368(AT)hotmail.com), Mar 19 2007
%C A008585 Multiples of 3. Positive members of this sequence are the third transversal 
               numbers (or 3-transversal numbers): Numbers of the 3rd column of 
               positive numbers in the square array of nonnegative and polygonal 
               numbers A139600. Also, numbers of the 3rd column in the square array 
               A057145. - Omar E. Pol (info(AT)polprimos.com), May 02 2008
%C A008585 Numbers n for which polynomial 27*x^6-2^n is factorizable. [From Artur 
               Jasinski (grafix(AT)csl.pl), Nov 01 2008]
%C A008585 Also n=0 mod (3); for n>0 first column [A144562] [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Jan 13 2009]
%C A008585 1/7 in base 2 notation = .001001001,...= 1/2^3 + 1/2^6 + 1/2^9 + ... 
               [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 24 2009]
%C A008585 Number of n permutations (n>=1) of 4 objects u, v, z, x, with repetition 
               allowed, containing n-1 u's. Example: if n=1 then n-1=zero (0) u, 
               a(1)=3 because we have v, z, x. if n=2 then n-1= one (1) u, a(2)=6 
               because we have vu, zu, xu, uv, uz, ux. if n=3 then n-1 =two (2) 
               u, a(3)=9 because we have vuu, uvu, uuv, zuu, uzu, uuz, xuu, uxu, 
               uux, etc. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 
               17 2009]
%C A008585 A165330(a(n)) = 153 for n > 0; subsequence of A165332. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009]
%H A008585 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A008585 A. S. Fraenkel, <a href="http://www.integers-ejcnt.org/">New games related 
               to old and new sequences</a>, INTEGERS, Electronic J. of Combinatorial 
               Number Theory, Vol. 4, Paper G6, 2004.
%H A008585 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=315">
               Encyclopedia of Combinatorial Structures 315</a>
%H A008585 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A008585 G.f.: 3x/(1-x)^2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 23 2008]
%F A008585 a(n)=A008486(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 28 2008]
%F A008585 a(n)=6*n-a(n-1)-9 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 23 2009]
%e A008585 For n=2, a(2)=6*2-0-9=3; n=3, a(3)=6*3-3-9=6; n=4, a(4)=6*4-6-9=9 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 23 2009]
%t A008585 aa = {}; Do[If[Length[FactorList[27 x^6 - 2^n]] > 2, AppendTo[aa, n]], 
               {n, 1, 100}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 01 
               2008]
%t A008585 Table[Binomial[n, 1]*3^1, {n, 0, 48}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 17 2009]
%o A008585 (Other) sage:[i for i in range(145) if gcd(3,i) == 3] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2009]
%Y A008585 Cf. A016957, A057145, A139600, A139606.
%Y A008585 Cf. A144562, A067076, A153238 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Jan 13 2009]
%Y A008585 A165340. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 17 2009]
%Y A008585 Sequence in context: A160943 A160930 A161351 this_sequence A031193 A008486 
               A135943
%Y A008585 Adjacent sequences: A008582 A008583 A008584 this_sequence A008586 A008587 
               A008588
%K A008585 nonn,new
%O A008585 0,2
%A A008585 N. J. A. Sloane (njas(AT)research.att.com).