A316232 - OEIS

%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