login
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.
4
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, 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, 6, 12, 13, 14, 0, 2, 7, 15, 0, 1, 2, 3, 7, 8, 15, 16
OFFSET
0,5
COMMENTS
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).
The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).
LINKS
FORMULA
T(n, 1) = 0.
T(n, 2) = A003842(n - 1) for any n > 0.
T(n, A361757(n)) = n.
EXAMPLE
Triangle T(n, k) begins:
n n-th row
-- -------------------------------------
0 0
1 0, 1
2 0, 2
3 0, 1, 2, 3
4 0, 1, 4
5 0, 2, 5
6 0, 1, 2, 3, 4, 5, 6
7 0, 2, 7
8 0, 1, 2, 3, 7, 8
9 0, 1, 4, 9
10 0, 2, 5, 7, 10
11 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
12 0, 1, 4, 12
PROG
(PARI) See Links section.
CROSSREFS
See A361755 for a similar sequence.
Sequence in context: A233292 A108456 A089107 * A364912 A321449 A180279
KEYWORD
nonn,base,tabf
AUTHOR
Rémy Sigrist, Mar 23 2023
STATUS
approved