|
| |
|
|
A128772
|
|
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.
|
|
4
|
|
|
|
1, 1, 2, 5, 13, 401, 481, 2287117, 78878513396841, 6030581597579643235137762961, 6865094956246907208106140720967823958952560128110027381, 45329249186513730009786407515216464213580508297931626801345253569136632512127458220781121772276418210005756761
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
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.
|
|
|
MAPLE
|
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: # R. J. Mathar, 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); # Alois P. Heinz, Aug 04 2009
|
|
|
MATHEMATICA
|
r[1] = r[2] = 1;
r[n_] := r[n] = FromContinuedFraction /@ Permutations[Array[r, n - 1]] // Max;
Table[a[n] = Numerator[r[n]]; Print[n, " ", a[n]]; a[n], {n, 1, 10}] (* Jean-François Alcover, May 18 2020 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
frac,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
