%I A033157
%S A033157 1,4,5,8,10,13,14,17,28,31,32,35,37,40,41,44,82,85,86,89,91,94,95,98,109,
%T A033157 112,113,116,118,121,122,125,244,247,248,251,253,256,257,260,271,274,275,
%U A033157 278,280,283,284,287,325,328,329,332,334,337,338,341,352,355,356,359,361
%N A033157 Begins with (1, 4); avoids 3-term arithmetic progressions.
%D A033157 Iacobescu, F. 'Smarandache Partition Type and Other Sequences.' Bull. 
               Pure Appl. Sci. 16E, 237-240, 1997.
%D A033157 H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, 
               Vol. 8, No. 1-2-3, 1997, 170-183.
%H A033157 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A033157 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NonarithmeticProgressionSequence.html">Link to a section of The World 
               of Mathematics.</a>
%F A033157 Partial sums of Da(n), where Da(n) is defined in the PARI program.
%F A033157 a(n) = A004793(n) + [n is even] + [ceiling(n/2) is even]. Proof by Lawrence 
               Sze. - Ralf Stephan, Nov 15 2004
%o A033157 (PARI) Da(n)=if(n<1,1,if(n%2==0,3*Da(n/2)+5-13*((n/2)%2)-6*((n/2)%4==2),
               3)) (from R. Stephan)
%Y A033157 See A004793 for a similar case.
%Y A033157 Cf. A092482.
%Y A033157 Row 2 of array in A093682.
%Y A033157 Sequence in context: A092022 A162902 A026491 this_sequence A059659 A140459 
               A139132
%Y A033157 Adjacent sequences: A033154 A033155 A033156 this_sequence A033158 A033159 
               A033160
%K A033157 nonn
%O A033157 1,2
%A A033157 N. J. A. Sloane (njas(AT)research.att.com).