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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.

%I A067576 #51 Apr 03 2023 09:16:33
%S A067576 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,
%T A067576 95,127,128,17,21,30,59,111,191,255,256,18,22,39,61,119,223,383,511,
%U A067576 512,20,25,43,62,123,239,447,767,1023,1024,24,26,45,79,125,247,479,895,1535,2047
%N 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.
%C A067576 This is a permutation of the positive integers; the inverse permutation is A356419. - _Jianing Song_, Aug 06 2022
%H A067576 Ivan Neretin, <a href="/A067576/b067576.txt">Table of n, a(n) for n = 1..8001</a> (126 antidiagonals)
%H A067576 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A067576 Array begins:
%e A067576         j=1  j=2  j=3  j=4  j=5  j=6
%e A067576   i=1:    1,   2,   4,   8,  16,  32, ...
%e A067576   i=2:    3,   5,   6,   9,  10,  12, ...
%e A067576   i=3:    7,  11,  13,  14,  19,  21, ...
%e A067576   i=4:   15,  23,  27,  29,  30,  39, ...
%e A067576   i=5:   31,  47,  55,  59,  61,  62, ...
%e A067576   i=6:   63,  95, 111, 119, 123, 125, ...
%t A067576 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
%Y A067576 Cf. A000120, A356419.
%Y A067576 T(n,n) gives A036563(n+1).
%Y A067576 The antidiagonals are read in the opposite direction from those in A066884.
%Y A067576 Antidiagonal sums give A361074.
%Y A067576 Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691.
%K A067576 base,easy,nonn,tabl
%O A067576 1,2
%A A067576 _Robert G. Wilson v_, Jan 30 2002