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A361755
Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.
3
0, 0, 1, 0, 2, 0, 3, 0, 1, 3, 4, 0, 5, 0, 1, 5, 6, 0, 2, 5, 7, 0, 8, 0, 1, 8, 9, 0, 2, 8, 10, 0, 3, 8, 11, 0, 1, 3, 4, 8, 9, 11, 12, 0, 13, 0, 1, 13, 14, 0, 2, 13, 15, 0, 3, 13, 16, 0, 1, 3, 4, 13, 14, 16, 17, 0, 5, 13, 18, 0, 1, 5, 6, 13, 14, 18, 19, 0, 2, 5, 7, 13, 15, 18, 20
OFFSET
0,5
COMMENTS
In other words, the n-th row lists the numbers k such that A003714(n) AND A003714(k) = A003714(k) (where AND denotes the bitwise AND operator).
The Zeckendorf representation is also known as the greedy Fibonacci representation (see A356771 for further details).
FORMULA
T(n, 1) = 0.
T(n, 2) = A139764(n) for any n > 0.
T(n, 2^A007895(n)) = n.
EXAMPLE
Triangle T(n, k) begins:
n n-th row
-- ------------------------
0 0
1 0, 1
2 0, 2
3 0, 3
4 0, 1, 3, 4
5 0, 5
6 0, 1, 5, 6
7 0, 2, 5, 7
8 0, 8
9 0, 1, 8, 9
10 0, 2, 8, 10
11 0, 3, 8, 11
12 0, 1, 3, 4, 8, 9, 11, 12
PROG
(PARI) See Links section.
CROSSREFS
See A361756 for a similar sequence.
Sequence in context: A362110 A236138 A363930 * A362755 A035614 A212138
KEYWORD
nonn,tabf,base
AUTHOR
Rémy Sigrist, Mar 23 2023
STATUS
approved