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Table read by rows: T(n, k) is the minimum number of applications of the map (x, y) -> (x + 1, 2*y) or the map (x, y) -> (2*x, y + 1) required to make both numbers in the pair equal, starting from (n, k), 0 <= k <= n.
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%I #26 Apr 06 2020 08:05:16

%S 0,3,0,5,2,0,8,3,1,0,7,4,6,10,0,6,3,3,1,7,0,5,9,2,9,6,10,0,6,5,10,3,1,

%T 6,10,0,12,7,4,5,9,10,6,10,0,11,12,6,12,3,1,7,6,10,0,10,10,13,2,5,9,

%U 11,10,6,10,0,9,6,9,10,12,3,1,7,10,6,10,0,12

%N Table read by rows: T(n, k) is the minimum number of applications of the map (x, y) -> (x + 1, 2*y) or the map (x, y) -> (2*x, y + 1) required to make both numbers in the pair equal, starting from (n, k), 0 <= k <= n.

%C First column is given by A304026.

%H Peter Kagey, <a href="/A304027/b304027.txt">Table of n, a(n) for n = 0..594</a> (first 33 rows)

%H Programing Puzzles & Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/questions/164085/bringing-a-pair-of-integers-to-equality">Bringing a pair of integers to equality</a>

%e T(5, 2) = 3 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| 3 0

%e 2| 5 2 0

%e 3| 8 3 1 0

%e 4| 7 4 6 10 0

%e 5| 6 3 3 1 7 0

%e 6| 5 9 2 9 6 10 0

%e 7| 6 5 10 3 1 6 10 0

%Y Cf. A304026.

%K nonn,tabl

%O 0,2

%A _Peter Kagey_, May 04 2018