A067576 Array T(i,j) read by downward antidiagonals, where T(i,j) is the j-th term whose binary expansion has i 1's.

1, 2, 3, 4, 5, 7, 8, 6, 11, 15, 16, 9, 13, 23, 31, 32, 10, 14, 27, 47, 63, 64, 12, 19, 29, 55, 95, 127, 128, 17, 21, 30, 59, 111, 191, 255, 256, 18, 22, 39, 61, 119, 223, 383, 511, 512, 20, 25, 43, 62, 123, 239, 447, 767, 1023, 1024, 24, 26, 45, 79, 125, 247, 479, 895, 1535, 2047

Offset: 1

Author

Robert G. Wilson v, Jan 30 2002

Keywords

• base
• easy
• nonn
• tabl

Comments

This is a permutation of the positive integers; the inverse permutation is A356419. - Jianing Song, Aug 06 2022

Examples

			Array begins:
        j=1  j=2  j=3  j=4  j=5  j=6
  i=1:    1,   2,   4,   8,  16,  32, ...
  i=2:    3,   5,   6,   9,  10,  12, ...
  i=3:    7,  11,  13,  14,  19,  21, ...
  i=4:   15,  23,  27,  29,  30,  39, ...
  i=5:   31,  47,  55,  59,  61,  62, ...
  i=6:   63,  95, 111, 119, 123, 125, ...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8001 (126 antidiagonals)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A356419.

T(n,n) gives A036563(n+1).

The antidiagonals are read in the opposite direction from those in A066884.

Antidiagonal sums give A361074.

Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691.

Programs

Mathematica

a = {}; Do[ a = Append[a, Last[ Take[ Select[ Range[2^13], Count[ IntegerDigits[ #, 2], 1] == j & ], i - j]]], {i, 2, 12}, {j, 1, i - 1} ]; a