|
%I #18 Mar 22 2020 08:01:18
%S 1,1,2,1,3,2,6,1,3,9,5,15,7,21,17,46,5,15,45,73,62,157,29,87,261,94,
%T 282,407,439,782,535,1605,206,618,1854,2137,3425,2986,7289,1669,5007,
%U 15021,170,510,1530,4590,13770,24493,16817,50451,6211,18633,55899
%N Smaller terms in the pairs of numbers (a < b) in the sequence {a,b}-> {Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]} with k=3 and the first pair {a=1,b=2}. See A075256.
%C Take any pair {a,b}. Each next pair is get by the rule {a,b} -> Sort[{Max[{a,b}]-Min[{a,b}],k*Min[{a,b}]]. Here k=3 and the first {a,b}={1,2}. For k = 2 there is a fixed point {a,b=2a}. For k > 2, are there any limits or cycles of the sequence {for some initial pair {a,b}?
%H Hugo Pfoertner, <a href="/A075257/b075257.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A075256(2*n-1).
%t ss=Table[0, {j, 100}]; s=ss[[1]]={1, 2}; Do[ss[[i]]=Sort[{Max[s]-Min[s], 3*Min[s]}]; s=ss[[i]], {i, 2, 100}]; Table[Flatten[ss][[i]], {i, 1, 199, 2}]
%o (PARI) my(x=1, y=2); print1(x,", "); for(n=2,53,my(mx=max(x,y),mi=min(x,y));x=min(mx-mi,3*mi);y=max(mx-mi,3*mi);print1(x,", ")) \\ _Hugo Pfoertner_, Mar 21 2020
%Y Cf. A075256, A075258.
%K nonn
%O 1,3
%A _Zak Seidov_, Sep 10 2002
|
