A289869 - OEIS

%I #14 Dec 07 2019 12:18:29

%S 0,2,1,6,3,3,8,7,5,4,18,9,9,6,9,20,19,11,10,11,10,24,21,21,12,15,12,

%T 12,26,25,23,22,17,16,14,13,54,27,27,24,27,18,18,15,27,56,55,29,28,29,

%U 28,20,19,29,28,60,57,57,30,33,30,30,21,33,30,30,62,61,59

%N Square array T(n,k) (n>=0, k>=0) read by antidiagonals downwards: T(n,k) = A005836(n) + 2*A005836(k).

%C If n and k have no common one bit in base 2 representation (n AND k = 0), then n = A289813(T(n,k)) and k = A289814(T(n,k)).

%C This sequence, when restricted to the pairs of numbers without common bits in base 2 representation, is the inverse of the function n -> (A289813(n), A289814(n)).

%H Rémy Sigrist, <a href="/A289869/b289869.txt">First 100 antidiagonals of array, flattened</a>

%e The table begins:

%e x\y:    0   1   2   3   4   5   6   7   8   9  ...

%e 0:      0   2   6   8   18  20  24  26  54  56 ...

%e 1:      1   3   7   9   19  21  25  27  55  57 ...

%e 2:      3   5   9   11  21  23  27  29  57  59 ...

%e 3:      4   6   10  12  22  24  28  30  58  60 ...

%e 4:      9   11  15  17  27  29  33  35  63  65 ...

%e 5:      10  12  16  18  28  30  34  36  64  66 ...

%e 6:      12  14  18  20  30  32  36  38  66  68 ...

%e 7:      13  15  19  21  31  33  37  39  67  69 ...

%e 8:      27  29  33  35  45  47  51  53  81  83 ...

%e 9:      28  30  34  36  46  48  52  54  82  84 ...

%e ...

%o (PARI) T(n,k) = fromdigits(binary(n),3) + 2*fromdigits(binary(k),3)

%o (Python)

%o def T(n, k): return int(bin(n)[2:], 3) + 2*int(bin(k)[2:], 3)

%o for n in range(11): print [T(k, n - k) for k in range(n + 1)] # _Indranil Ghosh_, Aug 03 2017

%Y Cf. A005836, A289813, A289814.

%K nonn,tabl,base

%O 1,2

%A _Rémy Sigrist_, Jul 14 2017