Search: id:A129082
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%I A129082
%S A129082 1,3,11,25,123,53,275,581,5898,6337,81839,52193,794409,929481,611743,
%T A129082 1609819,24076913,6686545,176364550,32690593,9049485,10684919,281305624,
%U A129082 439838742,20192641459,17176118816,107883019372,142161870055
%N A129082 a(n) = numerator of b(n): b(n) = the maximum possible value for a continued 
               fraction whose terms are a permutation of the terms of the simple 
               continued fraction for H(n) = sum{k=1 to n} 1/k, the n-th harmonic 
               number.
%H A129082 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A129082 The continued fraction for H(5) = 137/60 is [2;3,1,1,8]. The maximum 
               value a continued fraction can have with these same terms in some 
               order is [8;1,3,1,2] = 123/14.
%p A129082 H := proc(n) add(1/k,k=1..n) ; end: 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 := numtheory[cfrac](H(n),'quotients') 
               ; rp := combinat[permute](rL) ; m := Ltoc(rL) ; for L in rp do m 
               := max(m, Ltoc(L)) ; od: m ; fi; end: A129082 := proc(n) numer(r(n)) 
               ; end: for n from 1 do printf("%d,\n", A129082(n)) ; od: [From R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2009]
%p A129082 Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009: 
               (Start)
%p A129082 with (numtheory): H:= proc(n) option remember; `if` (n=1, 1, H(n-1)+1/
               n) end:
%p A129082 r:= proc(l) local j; infinity; for j from nops(l) to 1 by -1 do l[j]+1/
               % od end:
%p A129082 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:
%p A129082 a:= n-> numer (r (sh (sort (cfrac (H(n), 'quotients'))))): seq (a(n), 
               n=1..40); (End)
%o A129082 (MAGMA) Q:=Rationals(); [ Numerator(Max([ r: r in R ])) where R:=[ c[1,
               1]/c[2,1]: c in C ] where C:=[ Convergents(s): s in S ] where S:=Seqset([ 
               [m(p[i]):i in [1..#x] ]: p in P ]) where m:=map< x->y | [<x[i],y[i]>
               :i in [1..#x] ] > where P:=Permutations(Seqset(x)) where x:=[1..#y]: 
               y in [ ContinuedFraction(h): h in [ &+[ 1/k: k in [1..n] ]: n in 
               [1..8] ] ] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jul 31 2009]
%Y A129082 Cf. A129083, A129084, A129085.
%Y A129082 Sequence in context: A056106 A147382 A164303 this_sequence A060746 A111935 
               A001008
%Y A129082 Adjacent sequences: A129079 A129080 A129081 this_sequence A129083 A129084 
               A129085
%K A129082 frac,nonn
%O A129082 1,2
%A A129082 Leroy Quet Mar 28 2007
%E A129082 6 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 
               2009
%E A129082 Extended byond a(12) Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 
               2009

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