Search: id:A143487
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%I A143487
%S A143487 4,3,3,3,2,2,2,4,4,2,2,2,1,1,1,4,4,1,1,1,3,3,3,4,4,3,3,3,2,2,2,4,4,2,2,
%T A143487 2,1,1,1,4,4,1,1,1,3,3,3,4,4,3,3,3,2,2,2,4,4,2,2,2,1,1,1,4,4,1,1,1,3,3,
%U A143487 3,4,4,3,3,3,2,2,2,4,4,2,2,2,1,1,1,4,4,1,1,1,3,3,3,4,4,3,3,3,2,2,2,4,4
%N A143487 "Fourth down, Extream [sic] between the two farthest Bells from it" in 
               bell-ringing is a sequence of permutations p_1=(1,2,3,4), p_2=(1,
               2,4,3], .. which runs through all permutations of {1,2,3,4} with 
               period 24; sequence gives number in position 4 of n-th permutation.
%C A143487 Start with (1,2,3,4), i.e. the first permutation of {1,2,3} followed 
               by 4; then for each next permutation, transpose 4 one to the left; 
               if at position 1, replace {1,2,3} recursively by the next permutation 
               of these numbers. Thereafter, for each next permutation, transpose 
               4 to the right. And so on.
%H A143487 <a href="http://www.gutenberg.org/files/18567/18567-h/18567-h.htm">The 
               Project Gutenberg EBook of Tintinnalogia, or, the Art of Ringing, 
               by Richard Duckworth and Fabian Stedman</a>
%H A143487 <a href="Sindx_Be.html#bell_ringing">Index entries for sequences related 
               to bell ringing</a>
%F A143487 Period 24.
%p A143487 ring:= proc(k::nonnegint) local p,i,left,l,nf,ini; if k<=1 then proc() 
               [1$k] end else ini := proc() p:= ring(k-1); i:= k; left:= true; l:= 
               p(); nf:= k! end; ini(); proc() local ll; ll:= [seq(l[t], t=1..(i-1)), 
               k, seq(l[t], t=i..(k-1))]; if left then if i>1 then i:= i-1 else 
               left:= false; l:=p() fi else if i<k then i:= i+1 else left:= true; 
               l:=p() fi fi; nf:= nf-1; if nf = 0 then ini() fi; ll end fi end: 
               bell := proc(k) option remember; local p; p:= ring(k); [seq(p(), 
               i=1..k!)] end: a := n-> bell(4)[modp(n-1,24)+1][4]: seq (a(n), n=1..121);
%Y A143487 Cf. A143484-A143490, A090281.
%Y A143487 Sequence in context: A016502 A117691 A171627 this_sequence A031350 A031353 
               A085415
%Y A143487 Adjacent sequences: A143484 A143485 A143486 this_sequence A143488 A143489 
               A143490
%K A143487 nonn
%O A143487 1,1
%A A143487 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 19 2008

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