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Search: id:A128774
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| A128774 |
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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. |
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4
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| 1, 1, 2, 4, 25, 416, 486098, 162537896768, 14630088002962344485338, 739175469608148343094159739813706354064860288, 15105149005060355385076902252968126357000941646823210191645645116442975494737766\ 02061398338
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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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.
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MAPLE
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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]
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]
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CROSSREFS
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Cf. A128772, A128773, A128775.
Sequence in context: A162125 A162126 A162118 this_sequence A129894 A028386 A155120
Adjacent sequences: A128771 A128772 A128773 this_sequence A128775 A128776 A128777
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet Mar 27 2007
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EXTENSIONS
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3 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2009
a(10) - a(11) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009
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