Search: id:A140778
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%I A140778
%S A140778 1,3,7,12,18,8,17,28,13,27,43,19,39,60,22,45,70,26,55,85,31,63,96,34,69,
%T A140778 105,37,77,118,42,88,135,48,97,147,52,103,156,56,113,171,59,120,184,65,
%U A140778 131,198,71,143,216,74,149,227,79,159,240,82,165,249,86,175,265,91,183
%N A140778 a(n) is the smallest positive integer such that no number occurs twice 
               in the sequence and its absolute first differences.
%C A140778 This sequence and its first differences include every positive integer 
               (exactly once).
%e A140778 For a(5), the sequence to that point is [1,3,7,12], with absolute differences 
               [2,4,5]. The next number cannot be 6, because then 6 would be in 
               both the sequence and the first differences. Since all values smaller 
               than 6 are taken, the difference must be positive and at least 6. 
               A difference of 6 works, a(5) = 18.
%o A140778 (PARI) IsInList(v, k) = for(i=1,#v,if(v[i]==k,return(1)));return(0) IsInDiff(v, 
               k) = for(i=2,#v,if(abs(v[i]-v[i-1])==k,return(1)));return(0) NextA140778(v)={ 
               local(i,d); if(#v==0,return(1)); i=2; while(1, d=abs(i-v[ #v]); if(!(i==d 
               || IsInList(v,i) || IsInDiff(v,i) || IsInList(v,d) || IsInDiff(v,
               d)), return(i)); i++) } v=[];for(i=1,100,v=concat(v,NextA140778(v)));
               v
%Y A140778 Cf. A140779, A081145.
%Y A140778 See also A005228, A030124, A037257, A037258, A037259, A061577.
%Y A140778 Sequence in context: A141205 A084582 A072098 this_sequence A095115 A141214 
               A027379
%Y A140778 Adjacent sequences: A140775 A140776 A140777 this_sequence A140779 A140780 
               A140781
%K A140778 easy,nonn
%O A140778 1,2
%A A140778 Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 29 2008

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