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

0,6

Links

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

Example

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;
...

Mathematica

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

Prog

(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)); );

Crossrefs

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

Sequence in context: A189768 A362327 A350168 * A336820 A099173 A293377

Adjacent sequences: A262878 A262879 A262880 * A262882 A262883 A262884

Keyword

nonn,base,tabl

Author

Michel Marcus, Oct 04 2015

Status

approved