A304026 Starting from (0, n), the minimum number of applications of the map (x, y) -> (x + 1, 2*y) or (x, y) -> (2*x, y + 1) required to make both numbers in the pair equal.

0, 3, 5, 8, 7, 6, 5, 6, 12, 11, 10, 9, 12, 11, 11, 10, 10, 9, 8, 16, 15, 14, 13, 12, 12, 11, 10, 9, 8, 7, 9, 10, 13, 12, 11, 12, 12, 12, 11, 10, 11, 14, 13, 12, 11, 10, 9, 17, 16, 15, 16, 15, 16, 17, 16, 15, 14, 17, 16, 15, 14, 13, 12, 12, 11, 10, 16, 15, 16

Offset

0,2

Comments

The number found after doing the steps is divisible by 4. - David A. Corneth, May 07 2018

From Robert G. Wilson v, May 12, 2018: (Start)

Records: 3, 5, 8, 12, 16, 17, 19, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 57, 75, 102, ..., .

First occurrence of k=0,1,2,... or -1 if no such value exists: 0, -1, -1, 1, -1, 2, 5, 4, 3, 11, 10, 9, 8, 22, 21, 20, 19, 47, 88, 87, 109, 108, 107, 180, 216, 358, 356, 368, 689, 729, 730, 985, ..., .

Last occurrence of k=0,1,2,... or -1 if no such value exists: 1, -1, -1, 2, -1, 7, 8, 30, 29, 125, 127, 508, 507, 2043, 2046, ... . [It looks like these numbers need to be reduced by 1. - Editors, Jun 10 2018]

(End)

Links

David A. Corneth, Table of n, a(n) for n = 0..9999 (first 351 terms from Peter Kagey)

Programing Puzzles & Code Golf Stack Exchange, Bringing a pair of integers to equality.

Example

For n = 2, the 5 steps are: (0,2) -> (1,4) -> (2,5) -> (3,10) -> (6,11) -> (12,12).

Mathematica

g[n_, k_] := Fold[ If[ Mod[#2, 2] == 0, 2 #, # + 1] &, n, k]; f[0] = 0; f[n_] := Block[{i = 1, id, idc}, While[id = IntegerDigits[i, 2]; idc = Mod[id + 1, 2]; 0 < Mod[i, 4] < 3 || g[0, id] != g[n, idc] && g[n, id] != g[0, idc], i++]; Length@ id]; Array[f, 69, 0] (* Robert G. Wilson v, May 08 2018 *)

Crossrefs

Cf. A304027.

Sequence in context: A368741 A021740 A172370 * A110641 A121729 A072105

Adjacent sequences: A304023 A304024 A304025 * A304027 A304028 A304029

Keyword

nonn,look

Author

Peter Kagey, May 04 2018

Status

approved