A066884 Square array read by upward antidiagonals where the n-th row contains the positive integers with n binary 1's.

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

Offset: 1

Author

Jared Benjamin Ricks (jaredricks(AT)yahoo.com), Jan 21 2002

Keywords

• nonn
• tabl
• base

Comments

This is a permutation of the positive integers; the inverse permutation is A067587.

Examples

			Column: 1   2   3   4   5   6
-----------------------------
Row 1:| 1   2   4   8  16  32
Row 2:| 3   5   6   9  10  12
Row 3:| 7  11  13  14  19  21
Row 4:|15  23  27  29  30  39
Row 5:|31  47  55  59  61  62
Row 6:|63  95 111 119 123 125
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8001 (126 antidiagonals)
• Vladimir Dobric, M. Skyers, and L. J. Stanley, Polynomial Time Computable Triangular Arrays For Almost Sure Convergence, arXiv preprint arXiv:1603.04896 [math.PR], 2016. [Shows that this sequence is in P-TIME]
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A067587.

Selected rows: A000079 (1), A018900 (2), A014311 (3), A014312 (4), A014313 (5), A023688 (6), A023689 (7), A023690 (8), A023691 (9), A038461 (10), A038462 (11), A038463 (12). For decimal analogs, see A011557 and A038444-A038452.

Selected columns: A000225 (1), A055010 (2).

Selected diagonals: A036563 (main), A000918 (1st upper), A153894 (2nd upper). [Franklin T. Adams-Watters, Apr 22 2009]

Cf. A067576 (the same array read by downward antidiagonals).

Antidiagonal sums give A361074.

Programs

Mathematica

a = {}; Do[ a = Append[a, Last[ Take[ Take[ Select[ Range[2^12], Count[ IntegerDigits[ #, 2], 1] == j - i + 1 & ], j], i]]], {j, 1, 11}, {i, 1, j}]; a

Extensions

Corrected and extended by Henry Bottomley, Jan 27 2002