Search: id:A128774
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%I A128774
%S A128774 1,1,2,4,25,416,486098,162537896768,14630088002962344485338,
%T A128774 739175469608148343094159739813706354064860288,
%U A128774 1510514900506035538507690225296812635700094164682321019164564511644297549473776602061398338
%N A128774 a(n) = numerator of r(n): r(1)=1, r(n+1) = [b(1,n);b(2,n),...,b(n,n)], 
               a continued fraction of rational terms, where {b(k,n)} is the permutation 
               of the first n terms of {r(k)} such that r(n+1) is minimized.
%H A128774 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A128774 The first 5 terms of {r(k)} are: 1,1,2,4/3,25/18. The continued fraction, 
               whose terms are the permutation of the first 5 terms of {r(k)} which 
               leads to the smallest r(6), is [1;2,1,25/18,4/3] = 416/303.
%p A128774 Ltoc := proc(L) numtheory[nthconver](L,nops(L)-1) ; end: r := proc(n) 
               option remember ; local m,rL,rp,L ; if n = 1 then 1; else rL := [seq(procname(i),
               i=1..n-1)] ; rp := combinat[permute](rL) ; m := Ltoc(rL) ; for L 
               in rp do m := min(m, Ltoc(L)) ; od: m ; fi; end: A128774 := proc(n) 
               numer(r(n)) ; end: for n from 1 do printf("%d,\n", A128774(n)) ; 
               od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2009]
%p A128774 tor:= proc(l) local j; infinity; for j from nops(l) to 1 by -1 do l[j]+1/
               % od end: hs:= proc(l) local ll, h, s, m; ll:= []; h:= nops(l); s:= 
               1; m:= s; while s<=h do ll:= [ll[], l[m]]; if m=h then h:= h-1; m:= 
               s else s:= s+1; m:= h fi od; ll end: r:= proc(n) option remember; 
               local j; `if` (n=1, 1, tor (hs (sort ([seq(r(j), j=1..n-1)])))) end: 
               a:= n-> numer (r(n)): seq (a(n), n=1..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 04 2009]
%Y A128774 Cf. A128772, A128773, A128775.
%Y A128774 Sequence in context: A162125 A162126 A162118 this_sequence A129894 A028386 
               A155120
%Y A128774 Adjacent sequences: A128771 A128772 A128773 this_sequence A128775 A128776 
               A128777
%K A128774 frac,nonn
%O A128774 1,3
%A A128774 Leroy Quet Mar 27 2007
%E A128774 3 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 
               2009
%E A128774 a(10) - a(11) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 
               2009

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