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A289869
Square array T(n,k) (n>=0, k>=0) read by antidiagonals downwards: T(n,k) = A005836(n) + 2*A005836(k).
2
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
1,2
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)).
EXAMPLE
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 ...
...
PROG
(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
CROSSREFS
KEYWORD
nonn,tabl,base
AUTHOR
Rémy Sigrist, Jul 14 2017
STATUS
approved