Search: id:A079934
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%I A079934
%S A079934 1,3,5,10,17,29,46,99,169,268,577,985,1562,3363,5741,9104,19601,33461,
%T A079934 53062,114243,195025,309268,665857,1136689,1802546,3880899,6625109,
%U A079934 10506008,22619537,38613965,61233502,131836323,225058681,356895004
%N A079934 Greedy frac multiples of sqrt(2): a(1)=1, sum(n>0,frac(a(n)*x))=1 at 
               x=sqrt(2).
%C A079934 The n-th greedy frac multiple of x is the smallest integer that does 
               not cause sum(k=1..n,frac(a(k)*x)) to exceed unity; an infinite number 
               of terms appear as the denominators of the convergents to the continued 
               fraction of x.
%F A079934 For n>0, a(3n) = A000129(2n+1), a(3n+2) = a(3n) + A000129(2n+2) and a(3n+4) 
               = a(3n+2) + a(3n+3). Also a(3n) = ceil((3+2*sqrt(2))^n*(2+sqrt(2))/
               4). a(3n+2)/a(3n+1) -> 1/sqrt(2); a(3n+1)/a(3n) -> 3-sqrt(2); a(3n)/
               a(3n-1) -> (8+5*sqrt(2))/7.
%e A079934 a(4) = 10 since frac(1x) + frac(3x) + frac(5x) + frac(10x) < 1, while 
               frac(1x) + frac(3x) + frac(5x) + frac(k*x) > 1 for all k>5 and k<10.
%Y A079934 Cf. A000129 (Pell numbers), A078343, A079935, A079936.
%Y A079934 Sequence in context: A000990 A129361 A062773 this_sequence A005403 A018072 
               A090170
%Y A079934 Adjacent sequences: A079931 A079932 A079933 this_sequence A079935 A079936 
               A079937
%K A079934 nonn
%O A079934 1,2
%A A079934 Benoit Cloitre (benoit7848c(AT)orange.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jan 20 2003

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