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Results tagged with integer-sequences
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user 3684
For questions about sequences of integers. References are often made to the online resource oeis.org.
2
votes
What are non-trivial facts about the sequence of averages of digits of an integer sequence?
Iekata Shiokawa, On the sum of digits of prime numbers, Proc Japan Acad 50 (1974) 551-554, proved $$\sum_{p\le x}A_r(p)={r-1\over2}{x\over\log r}+O\left(x\left({\log\log x\over\log x}\right)^{1/2}\rig …
- 39.9k
5
votes
Put as many points as possible in an equilateral triangle of side 1 with their minimal dista...
This is related to problems of packing circles into an equilateral triangle, and covering an equilateral triangle by circles. Some data on these problems is available at https://erich-friedman.github. …
- 39.9k
2
votes
Accepted
constructing a covering system of congruences?
Here's one way to construct those covers.
Every integer is $0\bmod2$ or $1\bmod2$. Keep one of those congruences, doesn't matter which one, say, $0\bmod2$, and go to work on the other one.
Every i …
- 39.9k
3
votes
Covering system of congruences with specific properties?
Given any finite set $n_1,\dots,n_r$ of moduli, there is an odd, nonsquare number $a$ such that the Legendre/Jacobi symbol $(a|n_i)=1$ for all $i$. You can't cover that $a$.
Give it up, asad – quit …
- 39.9k
9
votes
Longest coinciding pair of integer sequences known
For what it's worth, the OEIS has 99 sequences containing the string 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35, which is all I had the patience to …
- 39.9k
10
votes
Find a formula for the recurrent sequence $q_{n+1}=q_n(q_n+1)+1$
The sequence (at any rate, the case $q_0=1$) has been studied, and references are given at OEIS. The closest thing to a formula given there is $a(n) = [c^{2^n}]$ for $n > 0$, where $c = 1.385089248334 …
- 39.9k
2
votes
Computationally challenging integer sequences
A semi-magic square of order $n$ is an $n\times n$ matrix with nonnegative integer entries, with all row sums and all column sums equal, e.g.,
$$
A_3=\pmatrix{2&2&3\cr3&3&1\cr2&2&3\cr}
$$
We write $c( …
- 39.9k