%I A123684
%S A123684 1,1,4,2,7,3,10,4,13,5,16,6,19,7,22,8,25,9,28,10,31,11,34,12,37,13,40,
%T A123684 14,43,15,46,16,49,17,52,18,55,19,58,20,61,21,64,22,67,23,70,24,73,25,
%U A123684 76,26,79,27,82,28,85,29,88,30,91,31,94,32,97,33,100,34,103,35,106,36
%N A123684 Alternate A016777(n) with A000027(n).
%C A123684 a(n) is a diagonal of Table A123685.
%F A123684 G.f.: x*(1+x+2*x^2)/((1-x)^2*(1+x)^2); a(n) = n - 1/4 - (1/2*n - 1/4)*(-1)^n; 
               a(2n-1) = A016777(n-1) = 3(n-1)+1, a(2n) = A000027(n) = n; a(n) = 
               A071045(n-1)+1; a(n) = A093005(n) - A093005(n-1) for n > 1; a(n) 
               = A105638(n+2) - A105638(n+1) for n > 1; a(n) = A092530(n) - A092530(n-1)-1; 
               a(n) = A031878(n+1) - A031878(n)-1. - Klaus Brockhaus, May 12 2007
%e A123684 The natural numbers begin 1,2,3,...A000027
%e A123684 Seq 3*n + 1 begins 1,4,7,10, ... A016777
%e A123684 so A123684 begins
%e A123684 1,1,4,2,7,3,10,...
%o A123684 (MAGMA) &cat[ [ 3*n-2, n ]: n in [1..36] ]; /* Klaus Brockhaus, May 12 
               2007 */
%o A123684 (PARI) 1. print(vector(72, n, if(n%2==0, n/2, (3*n-1)/2))); 2. print(vector(72, 
               n, n-1/4-(1/2*n-1/4)*(-1)^n)); /* Klaus Brockhaus, May 12 2007 */
%Y A123684 Cf. A000027, A016777, A123685, A071045, A093005, A105638, A092530, A031878.
%Y A123684 Sequence in context: A126091 A026189 A026213 this_sequence A002949 A130849 
               A138754
%Y A123684 Adjacent sequences: A123681 A123682 A123683 this_sequence A123685 A123686 
               A123687
%K A123684 easy,nonn
%O A123684 1,3
%A A123684 Alford Arnold (Alford1940(AT)aol.com), Oct 11 2006
%E A123684 More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 
               12 2007