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%I #14 Nov 08 2018 19:00:14
%S 0,4,1,12,4,2,16,8,4,3,16,12,36,164,4,16,8,12,6,68,5,16,108,8,132,52,
%T 228,6,32,20,164,16,8,60,260,7,100,44,20,36,164,268,68,292,8,100,332,
%U 44,420,20,10,100,76,324,9,100,132,524,12,44,196,420,332,84
%N Table read by rows: T(n, k) is the minimum number m such that (m, m) can be reached from A304027(n, k) applications of either (x, y) -> (x + 1, 2*y) or (x, y) -> (2*x, y + 1), starting from (n,k), where 0 <= k <= n.
%C T(n, k) is divisible by 4 whenever n or k is even.
%C Conjecture: T(n,k) is the minimum number m such that (m,m) can be reached from any number of applications of these maps.
%e T(5, 2) = 12 by the map (*2, +1) followed by two applications of the map (+1, *2): (5,2) -> (10,3) -> (11,6) -> (12,12).
%e Table begins:
%e n\k| 0 1 2 3 4 5 6 7
%e ---+----------------------------------------
%e 0| 0
%e 1| 4 1
%e 2| 12 4 2
%e 3| 16 8 4 3
%e 4| 16 12 36 164 4
%e 5| 16 8 12 6 68 5
%e 6| 16 108 8 132 52 228 6
%e 7| 32 20 164 16 8 60 260 7
%Y Cf. A304027.
%K nonn,tabl
%O 0,2
%A _Peter Kagey_, Jun 27 2018
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