For questions about sequences of integers. References are often made to the online resource oeis.org.

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4
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2answers
193 views

Databases for sequences indexed by partitions

Is there a database for sequences indexed by partitions similar to Sloane's OEIS? I mean, I am aware that in the OEIS there are some arrays indexed by partitions, but I feel as though most of such ...
1
vote
1answer
181 views

Nested Sequence of Integers

In some combinatorial research I came across the following nested sequence: $$\{a_n\}=\{1,1,3,1,7,3,17,1,35,7,77,3,157,17,331,1,663,35,1361,7,2729,77,5535,3,11073, \dots\}$$ which is not in the OEIS. ...
5
votes
0answers
393 views

Number of Configurations in the optimal Hanoi tower

There is a unique strategy how to move $n$ disks from the first rod to the second optimally and it takes $2^n-1$ steps, solution is obtained by simple recursion. I am interested into the following ...
0
votes
2answers
203 views

sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence. ...
11
votes
0answers
604 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 ...
9
votes
2answers
1k views

sequences with a fractal dimension

This is inspired by the self-similarity of the celebrated Golay-Rudin-Shapiro sequence, more exactly, of its alternating partial sums. (This latter one is oeis 020990). The pictures show the 550 first ...
2
votes
3answers
546 views

For any prime $p$, is there $C$ such that if $x\ge C$, then all but one integer among $x+1, x+2, \dots, x+p$ has Greatest Prime Factor $> p$

I apologize if this is a naive question about greatest prime factors (gpf). I was thinking about the sequence of integers where $\mathrm{gpf}(x) \le p$ where $p$ is any prime. Clearly, as $x$ ...
1
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1answer
299 views

Maximal difference between k randomly drawn numbers from 1 to n – Looking for formula to sequence

Hello! I have an interesting problem that seemed simple to me, but I'm unable to solve it on my own. Suppose I am drawing k numbers out of n numbers labeled from 1 to n. Considering all ...
3
votes
2answers
916 views

Which $n$ maximize $G(n)=\frac{\sigma(n)}{n \log \log n}$?

By Robin's theorem $$G(n)=\frac{\sigma(n)}{n \log \log n}$$ is bounded by $e^\gamma \approx 1.78107241799$ for $n>5040$ assuming Riemann hypothesis . For $n=\mathrm {lcm} (1,2 \dots k)$, $G(n)$ ...
-3
votes
2answers
682 views

An interesting, simple, sequence - surprised to find little material. [closed]

I've been considering this sequence: $$1,2,3,6,12,24,48,96,192,...$$ I've generated the sequence from the rule $$V_n=\sum_{0\leq i \lt n} V_i$$ $$V_0=1; V_1=2V_0=V_0+V_0$$ What interests me most, ...
7
votes
2answers
611 views

Maximal number of edges and triangular cells for n points in a triangular lattice

Consider a subset of $n$ points in an equilateral triangular lattice. Draw all the edges between nearest-neighbor points. What is the maximum, over all such subsets, of the number of edges? This ...
20
votes
3answers
1k views

Zeroes of the random Fibonacci sequence

Let X_n be the "random Fibonacci sequence," defined as follows: $X_0 = 0, X_1 = 1$; $X_n = \pm X_{n-1} \pm X_{n-2}$, where the signs are chosen by independent 50/50 coinflips. It is known that ...
14
votes
2answers
1k views

Some unpublished notes of Hofstadter

I'm looking for some unpublished notes called "Eta Lore," which are apparently related to a talk Douglas Hofstadter first gave at the Stanford Math Club in 1963. I know these notes exist because ...
3
votes
0answers
596 views

Least Prime Factor in a sequence of 2n consecutive integers

I was thinking about consecutive integers and I wondered if anyone had done work exploring whether a sequence of $2n$ consecutive integers (i.e. 101,102,103,...,100+2n) always contains at least one ...
7
votes
4answers
820 views

A Pascal's-triangle -like random process

I was exploring Pascal's triangle on a cylinder when I encountered this puzzle-like problem. It is surely elementary, but perhaps weekend-entertaining. Start with a permutation of $(1,2,3, \ldots, ...
11
votes
0answers
573 views

Is “OEIS A001935 Number of partitions with no even part repeated” efficiently computable $\mod 4$?

Is A001935 Number of partitions with no even part repeated efficiently computable $\mod 4$? I am interested because of this relation with sum of divisors of $8n+1$. $\sigma(8n+1) \equiv A001935(n) ...
8
votes
1answer
713 views

Up to $10^6$: $\sigma(8n+1) \mod 4 = OEIS A001935(n) \mod 4$ (Number of partitions with no even part repeated )

Up to $10^6$: $\sigma(8n+1) \mod 4 = OEIS A001935(n) \mod 4$ A001935 Number of partitions with no even part repeated Is this true in general? It would mean relation between restricted partitions ...
11
votes
1answer
620 views

Put as many points as possible in an equilateral triangle of side 1 with their minimal distance greater than 1/n

It is known by the pigeon-hole principle that: If we select $5$ points within an equilateral triangle with side $1$, there must be at least two whose distance apart is less than or equal to $1/2$. ...
5
votes
5answers
617 views

Can an integer or rational sequence satisfy some bounded order recurrence $\mod \ $ almost all primes but doesn't satisfy such in $\mathbb{Q}$?

Can an integer or rational sequence satisfy some bounded order recurrence $\mod \ $ almost all primes but doesn't satisfy such in $\mathbb{Q}$? The recurrences $\mod p$ can be different, possibly ...
15
votes
1answer
2k views

Conjecture on signed sum of integer fractions x/y from 1..N?

Here is a generalization of an integer challenge that was asked on Yahoo!Answers in 2009, I believe it could be original, defies induction and has exponential-complexity. Not aware of any theory that ...
11
votes
11answers
3k views

Longest coinciding pair of integer sequences known

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by ...