Search: id:A004793
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%I A004793
%S A004793 1,3,4,6,10,12,13,15,28,30,31,33,37,39,40,42,82,84,85,87,91,93,94,96,
%T A004793 109,111,112,114,118,120,121,123,244,246,247,249,253,255,256,258,271,
%U A004793 273,274,276,280,282,283,285,325,327,328,330,334,336,337,339,352,354
%N A004793 a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), 
               ..., a(n-1), k form an arithmetic progression.
%D A004793 Iacobescu, F. 'Smarandache Partition Type and Other Sequences.' Bull. 
               Pure Appl. Sci. 16E, 237-240, 1997.
%H A004793 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A004793 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 A004793 a(n) = (3-n)/2 + 2*floor(n/2) + sum(k=1, n-1, 3^A007814(k))/2 = A003278(n) 
               + [n is even], proved by Lawrence Sze, following a conjecture by 
               Ralf Stephan.
%F A004793 a(n) = b(n-1), with b(0)=1, b(2n)=3b(n)-2-3[n odd], b(2n+1)=3b(n)-3[n 
               odd].
%o A004793 (PARI) v[1]=1:v[2]=3:for(n=3,1000,f=2:m=v[n-1]+1:while(1, forstep(k=n-1,
               1,-1,if(v[k]<(m+1)/2,f=1:break):for(l=1,k-1,if(m-v[k]==v[k]-v[l],
               f=0:break)): if(f<2,break)): if(!f,m=m+1:f=2): if(f==1,break)):v[n]=m) 
               (Ralf Stephan)
%o A004793 (PARI) a(n)=if(n<1,1,if(n%2==0,3*a(n/2)-2-3*((n/2)%2),3*a((n-1)/2)-3*(((n-1)/
               2)%2))) (Ralf Stephan)
%Y A004793 Cf. A092482.
%Y A004793 Row 1 of array in A093682.
%Y A004793 Sequence in context: A047296 A137951 A082694 this_sequence A031132 A057477 
               A113887
%Y A004793 Adjacent sequences: A004790 A004791 A004792 this_sequence A004794 A004795 
               A004796
%K A004793 nonn
%O A004793 1,2
%A A004793 N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
%E A004793 Rechecked by David W. Wilson, Jun 04, 2002.

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