cp's OEIS Frontend

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

%I A066884 #38 Apr 14 2023 12:38:10
%S A066884 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,
%T A066884 19,12,64,255,191,111,59,30,21,17,128,511,383,223,119,61,39,22,18,256,
%U A066884 1023,767,447,239,123,62,43,25,20,512,2047,1535,895,479,247,125,79,45,26,24,1024
%N A066884 Square array read by upward antidiagonals where the n-th row contains the positive integers with n binary 1's.
%C A066884 This is a permutation of the positive integers; the inverse permutation is A067587.
%H A066884 Ivan Neretin, <a href="/A066884/b066884.txt">Table of n, a(n) for n = 1..8001</a> (126 antidiagonals)
%H A066884 Vladimir Dobric, M. Skyers, and L. J. Stanley, <a href="https://arxiv.org/abs/1603.04896">Polynomial Time Computable Triangular Arrays For Almost Sure Convergence</a>, arXiv preprint arXiv:1603.04896 [math.PR], 2016. [Shows that this sequence is in P-TIME]
%H A066884 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A066884 Column: 1   2   3   4   5   6
%e A066884 -----------------------------
%e A066884 Row 1:| 1   2   4   8  16  32
%e A066884 Row 2:| 3   5   6   9  10  12
%e A066884 Row 3:| 7  11  13  14  19  21
%e A066884 Row 4:|15  23  27  29  30  39
%e A066884 Row 5:|31  47  55  59  61  62
%e A066884 Row 6:|63  95 111 119 123 125
%t A066884 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
%Y A066884 Cf. A000120, A067587.
%Y A066884 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.
%Y A066884 Selected columns: A000225 (1), A055010 (2).
%Y A066884 Selected diagonals: A036563 (main), A000918 (1st upper), A153894 (2nd upper). [_Franklin T. Adams-Watters_, Apr 22 2009]
%Y A066884 Cf. A067576 (the same array read by downward antidiagonals).
%Y A066884 Antidiagonal sums give A361074.
%K A066884 nonn,tabl,base
%O A066884 1,2
%A A066884 Jared Benjamin Ricks (jaredricks(AT)yahoo.com), Jan 21 2002
%E A066884 Corrected and extended by _Henry Bottomley_, Jan 27 2002