

A323456


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.


3



2, 1, 4, 5, 6, 2, 8, 3, 9, 10, 3, 10, 12, 11, 13, 14, 4, 16, 5, 17, 18, 5, 6, 18, 20, 7, 19, 21, 22, 6, 20, 24, 7, 21, 25, 26, 7, 22, 26, 28, 23, 27, 29, 30, 8, 32, 9, 33, 34, 9, 10, 34, 36, 11, 35, 37, 38, 10, 12, 36, 40, 11, 13, 37, 41, 42, 11, 14, 38, 42
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OFFSET

1,1


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 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 17 2019


LINKS

Rémy Sigrist, Rows n = 1..1000, flattened


EXAMPLE

From 6 = 110 we can get 11 = 3, 1010 = 10, or 1100 = 12, so row 6 is {3,10,12}.
From 7 = 111 we can get 1011 = 11, 1101 = 13, or 1110 = 14, so row 7 is {11,13,14}.
The triangle begins:
2,
1, 4,
5, 6,
2, 8,
3, 9, 10,
3, 10, 12,
11, 13, 14,
4, 16,
5, 17, 18,
5, 6, 18, 20,
7, 19, 21, 22,
...


PROG

(PARI) row(n) = { my (r=Set(), w=0, s=0); while (n, my (v=1+valuation(n, 2)); r = setunion(r, Set(n*2^(w+1)+s)); if (v>1, r = setunion(r, Set(n*2^(w1)+s))); s += (n%(2^v))*2^w; w += v; n \= 2^v); r } \\ Rémy Sigrist, Jan 27 2019


CROSSREFS

Cf. A000120, A323455, A323465.
This is a base2 analog of A323286.
Sequence in context: A144774 A326056 A074720 * A326058 A262586 A058359
Adjacent sequences: A323453 A323454 A323455 * A323457 A323458 A323459


KEYWORD

nonn,tabf,base


AUTHOR

N. J. A. Sloane, Jan 17 2019


EXTENSIONS

More terms from Rémy Sigrist, Jan 27 2019


STATUS

approved



