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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
All the numbers in row n have the same binary weight (A000120) as n.
If k appears in row n, n appears in row k.
If we form a graph on the positive integers by joining k to n if k appears in row n, then there is a connected component for each weight 1, 2, ...
The largest number in row n is 2n.
The smallest number in the component containing n is 2^A000120(n)-1, and n is reachable from 2^A000120(n)-1 in A023416(n) steps. - Rémy Sigrist, Jan 26 2019
LINKS
EXAMPLE
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;
...
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 *)
CROSSREFS
Cf. A000120, A323286, A323455, A323456, A323466 (number of terms in each row), A323467 (minimal number in each row).
This is a base-2 analog of A323460.
Sequence in context: A100461 A302655 A316997 * A364780 A124904 A187500
KEYWORD
nonn,tabf,look,base
AUTHOR
N. J. A. Sloane, Jan 26 2019
EXTENSIONS
More terms from Rémy Sigrist, Jan 27 2019
STATUS
approved

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Last modified April 24 14:54 EDT 2024. Contains 371960 sequences. (Running on oeis4.)