**15**

votes

**10**answers

1k views

### Combinatorial Databases

At one point, I remember being excited by seeing the website Encyclopedia of Combinatorial Structures as an extension of Sloane's Online Integer Sequence Database site. Unfortunately, the site (ECS) ...

**13**

votes

**1**answer

790 views

### Wrong asymptotics of OEIS A000607?

Sequence A000607 in the Online Encyclopedia of Integer Sequences is the number of partitions of $n$ into prime parts. For example, there are $5$ partitions of $10$ into prime parts: $10 = 2 + 2 + 2 + ...

**37**

votes

**2**answers

1k views

### Numbers that are generic w.r.t. exponentiation

This is a follow-up to my old question Number of distinct values taken by $x\hat{\phantom{\hat{}}}x\hat{\phantom{\hat{}}}\dots\hat{\phantom{\hat{}}}x$ with parentheses inserted in all possible ways.
...

**20**

votes

**1**answer

507 views

### Busy Beaver modulo 2

There is well-known Rado's "Busy Beaver" sequence — the maximal number of marks which a halting Turing machine with n states, 2 symbols (blank, mark) can produce onto an initially blank two-way ...

**7**

votes

**2**answers

522 views

### How to cite a sequence from The On-Line Encyclopedia of Integer Sequences (OEIS)?

In my paper I want to provide a reference for a sequence (in this case - A001970) from The On-Line Encyclopedia of Integer Sequences (OEIS).
However, I couldn't find an official bib entry for it ...

**11**

votes

**0**answers

564 views

### Is OEIS A007018 really a subsequence of squarefree numbers?

A comment in A007018 a(n) = a(n-1)^2 + a(n-1), a(0)=1 claims
Subsequence of squarefree numbers (A005117). - Reinhard Zumkeller, Nov 15 2004
Is it really so?
As far as I know, it is open problem ...

**17**

votes

**1**answer

964 views

### Number of distinct values taken by $\alpha$ ^ $\alpha$ ^ $\dots$ ^ $\alpha$ with parentheses inserted in all possible ways, $\alpha\in\mathbf{Ord}$

Let $\alpha\in\mathbf{Ord}$ and $n\in\mathbb{N}^+$.
Let $F_\alpha(n)$ be the number of distinct values taken by ordinal exponentiation $\underbrace{\alpha \hat{\phantom{\hat{}}} \alpha ...

**0**

votes

**1**answer

185 views

### Understanding a sequence generation formula of the A064532

I'm trying to understand the formula presented for the sequence A064532 from the OEIS, looks like a recurrence relation with complex numbers:
$a(10i+j) = a(i) + a(j), etc.$
Sorry if its a simple ...

**18**

votes

**1**answer

1k views

### Number of distinct values taken by x^x^…^x with parentheses inserted in all possible ways

For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence A000081? Is it exactly the set of positive ...

**15**

votes

**2**answers

860 views

### Least number of non-zero coefficients to describe a degree n polynomial

I'd be grateful for a good reference on this, it feels like a classic subject yet I couldn't find much about it.
Polynomials in one variable of the form $x^n+a_{n-1}x^{n-1}+\dots +a_1 x+a_0$ can be ...