|
%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
|
