A323465 Irregular triangle read by rows: row n lists the numbers that can be obtained from the binary expansion of n by either deleting a single 0, or inserting a single 0 after any 1, or doing nothing.
1, 2, 1, 2, 4, 3, 5, 6, 2, 4, 8, 3, 5, 9, 10, 3, 6, 10, 12, 7, 11, 13, 14, 4, 8, 16, 5, 9, 17, 18, 5, 6, 10, 18, 20, 7, 11, 19, 21, 22, 6, 12, 20, 24, 7, 13, 21, 25, 26, 7, 14, 22, 26, 28, 15, 23, 27, 29, 30, 8, 16, 32, 9, 17, 33, 34, 9, 10, 18, 34, 36, 11, 19
Offset: 1
Examples
From 6 = 110 we can get 6 = 110, 11 = 3, 1010 = 10, or 1100 = 12, so row 6 is {3,6,10,12}.
From 7 = 111 we can get 7 = 111, 1011 = 11, 1101 = 13, or 1110 = 14, so row 7 is {7,11,13,14}.
The triangle begins:
1, 2;
1, 2, 4;
3, 5, 6;
2, 4, 8;
3, 5, 9, 10;
3, 6, 10, 12;
7, 11, 13, 14;
4, 8, 16;
5, 9, 17, 18;
5, 6, 10, 18, 20;
7, 11, 19, 21, 22;
6, 12, 20, 24;
7, 13, 21, 25, 26;
7, 14, 22, 26, 28;
15, 23, 27, 29, 30;
8, 16, 32;
...
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..8208
Crossrefs
Programs
-
Mathematica
r323465[n_] := Module[{digs=IntegerDigits[n, 2]} ,Map[FromDigits[#, 2]&, Union[Map[Insert[digs, 0, #+1]&, Flatten[Position[digs, 1]]], Map[Drop[digs, {#}]&, Flatten[Position[digs, 0]]], {digs}]]] (* nth row *) a323465[{m_, n_}] := Flatten[Map[r323465, Range[m, n]]] a323465[{1, 22}] (* Hartmut F. W. Hoft, Oct 24 2023 *)
Extensions
More terms from Rémy Sigrist, Jan 27 2019
Comments