A262881 Regular triangle where the n-th row lists the integers k between 0 and n ordered by increasing value of the Hamming weight of k, and if equal by increasing value of k.

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 4, 3, 0, 1, 2, 4, 3, 5, 0, 1, 2, 4, 3, 5, 6, 0, 1, 2, 4, 3, 5, 6, 7, 0, 1, 2, 4, 8, 3, 5, 6, 7, 0, 1, 2, 4, 8, 3, 5, 6, 9, 7, 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 7, 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 7, 11, 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11

Offset: 0

Author

Michel Marcus, Oct 04 2015

Keywords

• nonn
• base
• tabl

Examples

			Triangle starts:
0;
0, 1;
0, 1, 2;
0, 1, 2, 3;
0, 1, 2, 4, 3;
0, 1, 2, 4, 3, 5;
0, 1, 2, 4, 3, 5, 6;
0, 1, 2, 4, 3, 5, 6, 7;
0, 1, 2, 4, 8, 3, 5, 6, 7;
0, 1, 2, 4, 8, 3, 5, 6, 9, 7;
0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 7;
...
		

Links

• Michel Marcus, Table of n, a(n) for n = 0..2079 (64 rows)

Crossrefs

Cf. A000120 (Hamming weight), A262882 (right diagonal).

Programs

Mathematica

Table[SortBy[Range@ k, And[Total@ IntegerDigits[#, 2], k] &], {k, 10}] (* Michael De Vlieger, Oct 04 2015 *)

PARI

cmph(i, j) = if (hammingweight(i) != hammingweight(j), hammingweight(i) - hammingweight(j), i - j);
row(n) = my(v = vector(n+1, k, k-1)); vecsort(v, cmph);
tabl(nn) = for (n=0, nn, print(row(n)););