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Tagged with integer-sequences fibonacci-numbers
7 questions
1
vote
1
answer
77
views
Sequence derived from transform of a given vector (with Fibonacci as partial sums)
Let F_n be A000045 (i.e., Fibonacci numbers). Here
$$
F_n = F_{n-1} + F_{n-2}, \\
F_0 = 0, F_1 = 1
$$
Let $\operatorname{wt}(n)$ be A000120 (i.e., number of ones in the binary expansion of $n$). ...
- 4,948
2
votes
2
answers
242
views
Negated Fibonacci and the floor function
Let $F_n$ be A000045 (i.e., Fibonacci numbers). Here
$$
F_n = F_{n-1} + F_{n-2}, \\
F_0 = 0, F_1 = 1, \\
F_{-n} = (-1)^{n-1}F_n
$$
I conjecture that
$$
F_{-n} = \left\lfloor\frac{n+1}{2}\right\rfloor ...
- 4,948
1
vote
0
answers
125
views
On a Fibonacci and binary
Let F(n) be A000045 i.e. Fibonacci numbers. Here
$$
F(n) = F(n-1) + F(n-2), \\
F(0) = 0, F(1) = 1
$$
Let
$$
\ell(n) = \left\lfloor\log_2 n\right\rfloor
$$
Let
$$
T(n, k) = \left\lfloor\frac{n}{2^k}\...
- 4,948
4
votes
0
answers
156
views
The smallest sequence without differences among Fibonacci numbers
Given a subset $\mathcal S\subset \mathbb N\setminus\{0\}$
of (strictly) positive integers, we can consider subsets
$A$ of $\mathbb N$ (or $\mathbb Z$) with no differences in
$\mathcal S$.
Examples: ...
- 17.9k
4
votes
1
answer
217
views
Why do convoluted convolved Fibonacci numbers pop up from this triangle?
Start with this triangle (OEIS A118981). This triangle is simple to generate with the following recurrence relation (though $T(0,0)$ ends up different from the OEIS version):
$$
T(0,0) = 2;T(1,0) = 1;...
- 194
8
votes
1
answer
363
views
Possible small mistake in Bilu-Hanrot-Voutier paper on primitive divisors of Lehmer sequences (?)
I think that I might have spotted I small mistake (a missing $5$-defective Lehmer pair) in the classification of terms of Lehmer sequences without primitive divisors given in:
1 Bilu, Hanrot, and ...
- 65
7
votes
1
answer
286
views
On nontotient Fibonacci numbers
This question is related to sequence of numbers $t$ such that $F_{6t}$ is a nontotient where $F_n$ represents the sequence of Fibonacci numbers for $n\geq 0$.
The online encyclopedia Wikipedia has the ...
- 701