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

1,2

Comments

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

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

Example

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

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

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.

Sequence in context: A283940 A163255 A297932 * A171429 A191448 A191447

Adjacent sequences: A066881 A066882 A066883 * A066885 A066886 A066887

Keyword

nonn,tabl,base

Author

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

Extensions

Corrected and extended by Henry Bottomley, Jan 27 2002

Status

approved