A316232 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.

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, 228, 6, 32, 20, 164, 16, 8, 60, 260, 7, 100, 44, 20, 36, 164, 268, 68, 292, 8, 100, 332, 44, 420, 20, 10, 100, 76, 324, 9, 100, 132, 524, 12, 44, 196, 420, 332, 84

Offset

0,2

Comments

T(n, k) is divisible by 4 whenever n or k is even.

Conjecture: T(n,k) is the minimum number m such that (m,m) can be reached from any number of applications of these maps.

Links

Table of n, a(n) for n=0..63.

Example

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).
Table begins:
  n\k|    0    1    2    3    4    5    6    7
  ---+----------------------------------------
    0|    0
    1|    4    1
    2|   12    4    2
    3|   16    8    4    3
    4|   16   12   36  164    4
    5|   16    8   12    6   68    5
    6|   16  108    8  132   52  228    6
    7|   32   20  164   16    8   60  260    7

Crossrefs

Cf. A304027.

Sequence in context: A145369 A145370 A130322 * A366885 A212046 A232013

Adjacent sequences: A316229 A316230 A316231 * A316233 A316234 A316235

Keyword

nonn,tabl

Author

Peter Kagey, Jun 27 2018

Status

approved