Implementation of a few integer sequences from the OEIS.

# OEIS

## Project

This project is the implementation of a few sequences from the OEIS.

## Usage

To install it, run: pip install oeis.

### Command line usage

oeis can be used from command line as:

\$ oeis --help
usage: oeis [-h] [--list] [--start START] [--stop STOP] [--plot] [--random] [--file] [--dark-plot] [sequence]

Print a sweet sequence

positional arguments:
sequence       Define the sequence to run (e.g.: A181391)

optional arguments:
-h, --help     show this help message and exit
--list         List implemented series
--start START  Define the starting point of the sequence.
--stop STOP    End point of the sequence (excluded).
--plot         Print a sweet sweet sweet graph
--random       Pick a random sequence
--file         Generates a png of the sequence's plot
--dark-plot    Print a dark dark dark graph

Need a specific sequence?

\$ oeis A000108
# A000108

Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
Also called Segner numbers.

[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190]

Lazy? Pick one by random:

\$ oeis --random
# A000045

Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181]

Want to see something cool?

\$ oeis A133058 --plot --stop 1200

### Library usage

The oeis module expose sequences as Python Sequences:

>>> from oeis import A000045
>>> print(*A000045[:10], sep=", ")
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
>>> A000045[1] == A000045[2]
True
>>> A000045[100:101]
[354224848179261915075]

## Contributing

We are using the [black]((https://github.com/psf/black) coding style, and tox to run some tests, so after creating a venv, installing dev requirements via pip install requirements-dev.txt, run tox or tox -p auto (parallel), it should look like this:

\$ tox -p auto
✔ OK mypy in 11.807 seconds
✔ OK flake8 in 12.024 seconds
✔ OK black in 12.302 seconds
✔ OK py36 in 13.776 seconds
✔ OK py37 in 15.344 seconds
✔ OK py38 in 21.041 seconds
______________________________________ summary ________________________________________
py36: commands succeeded
py37: commands succeeded
py38: commands succeeded
flake8: commands succeeded
mypy: commands succeeded
black: commands succeeded
congratulations :)

There's two ways to implement a serie: by implementing it as a function, or by implementing it as a a generator.

### Implementing a serie from a function

For serie where the result only depend of the its position, like A004767 which is a(n) = 4*n + 3, it's straightforward as a function, use the @oeis.from_function() as a decorator to setup the plumbing:

@oeis.from_function()
def A004767(n: int) -> int:
"""Integers of a(n) = 4*n + 3."""
return 4 * n + 3

It has the advantage of having fast direct access:

print(A004767[1_000_000])

can be done by calling your function a single time.

Beware: No "offset correction" is done magically. If the offset is 1, don't expect your function to be called with n=0.

### Implementing a serie from a generator

Some series need the previous (or previouses) values to be computed, they can't easily be implemented as functions, you can implement them as generators, in this case use the @oeis.from_generator() decorator:

@oeis.from_generator()
def A000045() -> Iterable[int]:
"""Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1."""
a, b = (0, 1)
yield 0
while True:
a, b = b, a + b
yield a

Beware: Just yield the actual serie values, don't care about the offset by trying, for example, to return None or 0 to shift the results.

### Comparison

So, to be clear, those two implementations are strictly equivalent:

@oeis.from_generator()
def A008589() -> Iterable[int]:
"""Multiples of 7."""
return (n * 7 for n in count())
@oeis.from_function()
def A008589(n: int) -> int:
"""Multiples of 7."""
return n * 7

And if the offset were 1, only the generator would change to start at 1 (the function does not need to change, as 1 would be given as a parameter):

@oeis.from_generator(offset=1)
def A008589() -> Iterable[int]:
"""Multiples of 7."""
return (n * 7 for n in count(1))