A067576 - OEIS

%I #51 Apr 03 2023 09:16:33

%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,

%T 95,127,128,17,21,30,59,111,191,255,256,18,22,39,61,119,223,383,511,

%U 512,20,25,43,62,123,239,447,767,1023,1024,24,26,45,79,125,247,479,895,1535,2047

%N 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 This is a permutation of the positive integers; the inverse permutation is A356419. - _Jianing Song_, Aug 06 2022

%H Ivan Neretin, <a href="/A067576/b067576.txt">Table of n, a(n) for n = 1..8001</a> (126 antidiagonals)

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e Array begins:

%e         j=1  j=2  j=3  j=4  j=5  j=6

%e   i=1:    1,   2,   4,   8,  16,  32, ...

%e   i=2:    3,   5,   6,   9,  10,  12, ...

%e   i=3:    7,  11,  13,  14,  19,  21, ...

%e   i=4:   15,  23,  27,  29,  30,  39, ...

%e   i=5:   31,  47,  55,  59,  61,  62, ...

%e   i=6:   63,  95, 111, 119, 123, 125, ...

%t 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 Cf. A000120, A356419.

%Y T(n,n) gives A036563(n+1).

%Y The antidiagonals are read in the opposite direction from those in A066884.

%Y Antidiagonal sums give A361074.

%Y Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691.

%K base,easy,nonn,tabl

%O 1,2

%A _Robert G. Wilson v_, Jan 30 2002