A361074 -id:A361074 - cp's OEIS frontend

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

Robert G. Wilson v, Jan 30 2002

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

			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, ...

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

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.

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

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

Original entry on oeis.org

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

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

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

			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

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

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.

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

Corrected and extended by Henry Bottomley, Jan 27 2002

cp's OEIS Frontend

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.

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