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%I #15 Aug 03 2022 17:42:01
%S 0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,1,0,0,1,0,0,0,0,3,0,0,0,0,1,0,3,3,0,
%T 1,0,0,0,0,0,4,0,0,0,0,0,0,2,0,0,0,0,2,0,0,0,1,0,0,1,5,1,0,0,1,0,0,0,
%U 0,0,0,5,5,0,0,0,0,0,0,0,2,0,0,5,6,5,0
%N The terms in the Zeckendorf representation of T(n, k) correspond to the terms in common in the Zeckendorf representations of n and of k; square array T(n, k) read by antidiagonals, n, k >= 0.
%C This array has connections with the bitwise AND operator (A004198).
%H Rémy Sigrist, <a href="/A334348/b334348.txt">Table of n, a(n) for n = 0..11475</a> (antidiagonals 0..150)
%H Rémy Sigrist, <a href="/A334348/a334348.png">Colored representation of (x, y) for 0 <= x, y <= 1000</a> (where the hue is function of T(x, y))
%H Rémy Sigrist, <a href="/A334348/a334348.gp.txt">PARI program for A334348</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeckendorf's_theorem">Zeckendorf's theorem</a>
%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F T(n, k) = A022290(A003714(n) AND A003714(k)) (where AND denotes the bitwise AND operator, A004198).
%F T(n, 0) = 0.
%F T(n, n) = n.
%F T(n, k) = T(k, n).
%F T(m, T(n, k)) = T(T(m, n), k).
%e Square array begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
%e ---+----------------------------------------------
%e 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 1| 0 1 0 0 1 0 1 0 0 1 0 0 1 0
%e 2| 0 0 2 0 0 0 0 2 0 0 2 0 0 0
%e 3| 0 0 0 3 3 0 0 0 0 0 0 3 3 0
%e 4| 0 1 0 3 4 0 1 0 0 1 0 3 4 0
%e 5| 0 0 0 0 0 5 5 5 0 0 0 0 0 0
%e 6| 0 1 0 0 1 5 6 5 0 1 0 0 1 0
%e 7| 0 0 2 0 0 5 5 7 0 0 2 0 0 0
%e 8| 0 0 0 0 0 0 0 0 8 8 8 8 8 0
%e 9| 0 1 0 0 1 0 1 0 8 9 8 8 9 0
%e 10| 0 0 2 0 0 0 0 2 8 8 10 8 8 0
%e 11| 0 0 0 3 3 0 0 0 8 8 8 11 11 0
%e 12| 0 1 0 3 4 0 1 0 8 9 8 11 12 0
%e 13| 0 0 0 0 0 0 0 0 0 0 0 0 0 13
%o (PARI) See Links section.
%Y Cf. A003714, A022290, A004198, A332022, A332565.
%K nonn,tabl,look,base
%O 0,13
%A _Rémy Sigrist_, Apr 24 2020