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Search: id:A128775
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| A128775 |
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a(n) = denominator 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, 1, 3, 18, 303, 352995, 118129644339, 10630462562660994073419, 537130892590606689570311912256259162899177699, 10976150076559127031443927456653042207771825462696364375815354372263245469807717\ 06185955699
(list; graph; listen)
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OFFSET
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1,4
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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: A128775 := proc(n) denom(r(n)) ; end: for n from 1 do printf("%d, \n", A128775(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-> denom (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, A128774.
Sequence in context: A137223 A159640 A038061 this_sequence A102100 A083000 A118704
Adjacent sequences: A128772 A128773 A128774 this_sequence A128776 A128777 A128778
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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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