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%I #18 Mar 22 2020 08:01:22
%S 2,3,3,6,5,9,7,18,17,14,27,22,45,38,63,51,138,133,118,135,219,186,471,
%T 442,355,783,689,846,1221,1317,2346,1811,4815,4609,3991,5562,6411,
%U 10275,8958,21867,20198,15191,45063,44893,44383,42853,38263,41310
%N Larger terms of the pairs (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="/A075258/b075258.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A075256(2*n).
%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, 2, 200, 2}]
%o (PARI) my(x=1, y=2); print1(y,", ");for(n=2,48,my(mx=max(x,y),mi=min(x,y)); x=min(mx-mi,3*mi); y=max(mx-mi,3*mi); print1(y,", ")) \\ _Hugo Pfoertner_, Mar 21 2020
%Y Cf. A075256, A075257.
%K nonn
%O 1,1
%A _Zak Seidov_, Sep 10 2002
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