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A361756 Irregular triangle T(n, k), n >= 0, k = 1..A361757(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the dual Zeckendorf representation of k also appear in that of n.

%I A361756 #14 Mar 27 2023 03:42:43
%S A361756 0,0,1,0,2,0,1,2,3,0,1,4,0,2,5,0,1,2,3,4,5,6,0,2,7,0,1,2,3,7,8,0,1,4,
%T A361756 9,0,2,5,7,10,0,1,2,3,4,5,6,7,8,9,10,11,0,1,4,12,0,2,5,13,0,1,2,3,4,5,
%U A361756 6,12,13,14,0,2,7,15,0,1,2,3,7,8,15,16
%N A361756 Irregular triangle T(n, k), n >= 0, k = 1..A361757(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the dual Zeckendorf representation of k also appear in that of n.
%C A361756 In other words, the n-th row lists the numbers k such that A003754(1+n) AND A003754(1+k) = A003754(1+k) (where AND denotes the bitwise AND operator).
%C A361756 The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).
%H A361756 Rémy Sigrist, <a href="/A361756/b361756.txt">Table of n, a(n) for n = 0..9956</a> (rows for n = 0..377 flattened)
%H A361756 Rémy Sigrist, <a href="/A361756/a361756.gp.txt">PARI program</a>
%H A361756 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A361756 T(n, 1) = 0.
%F A361756 T(n, 2) = A003842(n - 1) for any n > 0.
%F A361756 T(n, A361757(n)) = n.
%e A361756 Triangle T(n, k) begins:
%e A361756   n   n-th row
%e A361756   --  -------------------------------------
%e A361756    0  0
%e A361756    1  0, 1
%e A361756    2  0, 2
%e A361756    3  0, 1, 2, 3
%e A361756    4  0, 1, 4
%e A361756    5  0, 2, 5
%e A361756    6  0, 1, 2, 3, 4, 5, 6
%e A361756    7  0, 2, 7
%e A361756    8  0, 1, 2, 3, 7, 8
%e A361756    9  0, 1, 4, 9
%e A361756   10  0, 2, 5, 7, 10
%e A361756   11  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
%e A361756   12  0, 1, 4, 12
%o A361756 (PARI) See Links section.
%Y A361756 See A361755 for a similar sequence.
%Y A361756 Cf. A003754, A003842, A356771, A361757.
%K A361756 nonn,base,tabf
%O A361756 0,5
%A A361756 _Rémy Sigrist_, Mar 23 2023