A289869 Square array T(n,k) (n>=0, k>=0) read by antidiagonals downwards: T(n,k) = A005836(n) + 2*A005836(k).

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, 12, 26, 25, 23, 22, 17, 16, 14, 13, 54, 27, 27, 24, 27, 18, 18, 15, 27, 56, 55, 29, 28, 29, 28, 20, 19, 29, 28, 60, 57, 57, 30, 33, 30, 30, 21, 33, 30, 30, 62, 61, 59

Offset: 1

Author

Rémy Sigrist, Jul 14 2017

Keywords

• nonn
• tabl
• base

Comments

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)).

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)).

Examples

			The table begins:
x\y:    0   1   2   3   4   5   6   7   8   9  ...
0:      0   2   6   8   18  20  24  26  54  56 ...
1:      1   3   7   9   19  21  25  27  55  57 ...
2:      3   5   9   11  21  23  27  29  57  59 ...
3:      4   6   10  12  22  24  28  30  58  60 ...
4:      9   11  15  17  27  29  33  35  63  65 ...
5:      10  12  16  18  28  30  34  36  64  66 ...
6:      12  14  18  20  30  32  36  38  66  68 ...
7:      13  15  19  21  31  33  37  39  67  69 ...
8:      27  29  33  35  45  47  51  53  81  83 ...
9:      28  30  34  36  46  48  52  54  82  84 ...
...
		

Links

• Rémy Sigrist, First 100 antidiagonals of array, flattened

Crossrefs

Cf. A005836, A289813, A289814.

Programs

PARI

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

Python

def T(n, k): return int(bin(n)[2:], 3) + 2*int(bin(k)[2:], 3)
for n in range(11): print([T(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, Aug 03 2017