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Search: id:A128772
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| A128772 |
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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 maximized. |
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4
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| 1, 1, 2, 5, 13, 401, 481, 2287117, 78878513396841, 6030581597579643235137762961, 6865094956246907208106140720967823958952560128110027381, 45329249186513730009786407515216464213580508297931626801345253569136632512127458\ 220781121772276418210005756761
(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: 1,1,2,5/2,13/4. The continued fraction, whose terms are the permutation of the first 5 terms of {r(k)} which leads to the largest r(6), is [13/4;1,5/2,1,2] = 401/100.
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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 m := -1 ; rL := [seq(procname(i), i=1..n-1)] ; rp := combinat[permute](rL) ; for L in rp do m := max(m, Ltoc(L)) ; od: m ; fi; end: A128772 := proc(n) numer(r(n)) ; end: for n from 1 do printf("%d, \n", A128772(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: sh:= proc(l) local ll, h, s, m; ll:= []; h:= nops(l); s:= 1; m:= h; 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 (sh (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. A128773, A128774, A128775.
Sequence in context: A090472 A120266 A065797 this_sequence A155838 A166405 A016737
Adjacent sequences: A128769 A128770 A128771 this_sequence A128773 A128774 A128775
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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(12) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009
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