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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 ...
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 $n$). ...
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 ...
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 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;...
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 ...