Questions tagged [oeis]
The acronym OEIS stands for the On-Line Encyclopedia of Integer Sequences, a well-known database of sequences of integers. It can be used for questions where this database is (or might be) relevant, mainly questions about particular sequences of integers. This tag is typically used in combination with other tags to make the scope of the question more precise; common examples of such tags include the top-level tags co.combinatorics and nt.number-theory.
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questions with no upvoted or accepted answers
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On the first sequence without triple in arithmetic progression
In this Numberphile video (from 3:36 to 7:41), Neil Sloane explains an amazing sequence:
It is the lexicographically first among the sequences of positive integers without triple in arithmetic ...
28
votes
0
answers
561
views
A sequence potentially consisting of only integers
I will first ask the question which can be stated very simply. Afterwards I will explain some motivation and give references to related sequences.
Consider the sequence defined by
$$b_n = \frac{(...
10
votes
0
answers
662
views
Is there a proof that OEIS-A002387 is $[ e^{n-\gamma} ]$?
Based on the comments on OEIS-A002387:
$a_{n}$ = 1, 2, 4, 11, 31, 83, 227, 616,...
it is likely, that the sequence $a_{n}$ coincides with $[ e^{n-\gamma} ]$ ,
where $\gamma$ is the Euler-Mascheroni ...
9
votes
0
answers
218
views
On the first sequence without collinear triple
Let $u_n$ be the sequence lexicographically first among the sequences of nonnegative integers with graphs without collinear three points (as for $a_n=n^2$ or $b_n=2^n$). It is a variation of that one.
...
7
votes
0
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My research paper involves computing additional terms of an existing OEIS sequence. Should I first amend the sequence or publish the results?
In the course of my research I computed terms of an existing OEIS sequence that are currently unknown. Having prepared my paper for publication, I am now faced with a (small) dilemma:
Do I first ...
7
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0
answers
211
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Increasing derivatives of recursively defined polynomials
Consider recursively defined polynomials $f_0(x)=x$ and $f_{n+1}(x)=f_n(x)−f_n'(x) x (1−x)$.
These polynomials have some special properties, for example $f_n(0)=0$, $f_n(1)=1$, and all $n+1$ roots of ...
7
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0
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Has anyone seen these binary trees (Catalan-type related to the Gegenbauer polynomials and Motzkin paths)?
The OEIS entry A121448 enumerates binary trees with $n$ edges and $k$ vertices with outdegree 1.
Has anyone seen these trees?
The o.g.f. for this entry, $G(x,t)$, is essentially a discriminant ...
5
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0
answers
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Formula and smallest solution for the A260711
Let $a(n)$ be A260711 without initial $0$ (i.e., numbers of the form $x^2 - y^2$ with $x > y$ where $x$ and $y$ are odd, $x + y$ is a power of $2$).
The sequence begins with
$$
8, 16, 32, 48, 64, ...
5
votes
0
answers
108
views
Hypergraphs with only disjoint perfect matchings
Let $H(n,r)$ be the set of $r$-uniform hypergraph with $n$ vertices that have only disjoint perfect matchings (i.e. every hyperedge only appears in at most one of the perfect matchings). Let $m(h(n,r))...
5
votes
0
answers
152
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Dirichlet eta function and Stirling Permutations
The Stirling permutations of order $k$ is a permutation of the multiset $1, 1, 2, 2, ..., k, k$. The Dirichlet $\eta$-function is a function closely related to the Riemann $\zeta$-function.
According ...
4
votes
0
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207
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Conjecture on tilting modules for an Auslander algebra
On page 13 of "Tilting modules for the Auslander algebra of $K(x)/x^n$" the author, Geuenich, suggests that the number ($p_{n,i}$) of isomorphism
classes of modules, occurring as the $i$-th summand of ...
3
votes
0
answers
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views
Guises of the refined Eulerian numbers, generated by tangent vectors (OEIS A145271)
The Eulerian numbers (OEIS A008292, not to be confused with the Euler numbers) pop up in numerous scenarios in combinatorics and advanced analysis, one as the components of the h-vectors of the ...
3
votes
0
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First to note/document the relation between permutohedra and multiplicative inversion
The relation between the refined face numbers of the permutohedra and the formal series expansion of the reciprocal of a function (exponential generating function, formal Taylor series) is given in ...
2
votes
0
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Possible subsequence of the A110978
Let $a(n)$ be A110978 i.e. odd integers that are nonprime, such that there exist two factors of each number that when multiplied together in binary base, do not ever require the use of a "carry&...
2
votes
0
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Why can one compute the sum of divisors of $n$ without factoring $n$?
Question links to paper
which states:
$$
\sigma(n)= \frac{6}{n^2(n-1)}\sum_{k=1}^{n-1}(3n^2-10k^2)\sigma(k)\sigma(n-k) \qquad (1)
$$
where $\sigma(n)$ is the sum of divisors of $n$.
Another similar ...
2
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0
answers
162
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Link of a power series by the Bernoullis for a Riccati equation to zonotopes?
On pg. 85 of The Rise and Development of Theory of Series up to the Early 1820s by Ferraro is a series soln. of
$$ d^2z/z = -x^2dx^2 $$
related to the reputed first appearance of a Riccati-type eqn.,...
2
votes
0
answers
183
views
Claim in OEIS will give some results about Legendre's and Brocard's conjectures
Claim in OEIS will give non-trivial results about Legendre's and Brocard's conjecture. The claim is very likely to be true, but I am not sure it is currently provable.
Brocard's conjecture
states ...
1
vote
0
answers
97
views
Subsequence such that $c(a(n))=2^n$
Let $a(n)$ be A060831, i.e., $\sum\limits_{k=1}^{n}\operatorname{number of odd divisors of} k$.
Let
$$\ell(n)=\left\lfloor\log_2 n\right\rfloor$$
Let
$$b(n,k)=2b(n,k-1)-2^{k-1}, b(n,0)=n$$
Let $c(n)$ ...
1
vote
0
answers
189
views
Closed form for partial sums of A103318
Let $a(n)$ be A103318, number of solutions $i$ in range $[0,n-1]$ to $i \equiv 0 \pmod {2^{n-i}}$: the sequence begins with
$$1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2$$
Also let's ...
1
vote
0
answers
89
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Recurrence for the viabin numbers of the self-conjugate integer partitions
Let $a(n)$ be A290254, the viabin numbers of the self-conjugate integer partitions, also defined as $\left\lbrace 0 \right\rbrace$ union fixed points of A059894, self-inverse permutation defined as ...
1
vote
0
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185
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Generalized Thomas Ordowski conjecture at OEIS sequence A002326
OEIS is the online encyclopedia of integer sequences, Here is the link to the sequence $A002326$: https://oeis.org/A002326
For $n\geq 0$, the $n$th term in the sequence is defined as: $a(n)$ equals ...
0
votes
0
answers
93
views
Formula for individual term of the Proth numbers
Let $a(n)$ be A080075 i.e. Proth numbers: of the form $k2^m + 1$ for $k$ odd, $m \geqslant 1$ and $2^m > k$.
The sequence begins with
$$
3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129
$$...
0
votes
0
answers
62
views
Simple non-recursive formula for inverse permutation to A316385
Let
$$
\ell(n)=\left\lfloor\log_2 n\right\rfloor
$$
Let
$$
f(n)=n+2^{\ell(n)+1}
$$
Let $a(n)$ be A316385, i.e. lexicographically earliest sequence of distinct positive terms such that for any $n > ...
0
votes
0
answers
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Conjectured congruence $A048852(n-1) \equiv p_n - p_{n-1} \pmod{4}$
Let $p_n$ denote the n-th prime. OEIS A048852
is shortly defined as "Difference between b^2 (in c^2=a^2+b^2) and product of successive prime pairs".
Numerical evidence for $3 \le n \le 52$, all of ...