OEISsequences 0.0.9

Python functions to generate OEIS sequences

oeis-sequences

Python functions to generate The On-Line Encyclopedia of Integer Sequences (OEIS) sequences

Requirements

Requires python >= 3.8

Installation

pip install OEISsequences

Usage

After installation, from oeis_sequences import OEISsequences will import all the functions accessible via OEISsequences.Axxxxxx. Alternatively, invidividual functions can be imported as from oeis_sequences.OEISsequences import Axxxxxx.

For each sequence, there are 3 different kinds of functions:

1. Functions named Axxxxxx: Axxxxxx(n) returns the n-th term of OEIS sequence Axxxxxx.

2. Functions named Axxxxxx_T: returns T(n,k) for OEIS sequences where the natural definition is a 2D table T.

3. Functions named Axxxxxx_gen: Axxxxxx_gen() returns a generator of OEIS sequence Axxxxxx.

The function Axxxxxx is best used to compute a single term. The generator Axxxxxx_gen is typically defined for sequences where terms are best generated sequentially and is best used when computing a sequence of consecutive terms.

For the generator, we can for example use list(islice(Axxxxxx_gen(),10)) to return the first 10 terms of sequence Axxxxxx Alternatively, setting gen = Axxxxxx_gen() and using next(gen) returns the next term of the sequence.

Given Axxxxxx_gen, one can define a function Axxxxxx as:

def Axxxxxx(n,offset=1): return next(islice(Axxxxxx_gen(),n-offset,None))

where a(offset) is the first term returned by the generator. This value of offset is the same as the offset parameter in the OEIS database.

Some functions Axxxxxx_gen contain an optional keyword startvalue that returns a generator of terms that are larger than or equal to startvalue.

For some sequences, e.g. A269483, both types of functions Axxxxxx and Axxxxxx_gen are provided.

Examples

Least power of 3 having exactly n consecutive 7's in its decimal representation.

from oeis_sequences.OEISsequences import A131546
print(A131546(5))
>> 721

Minimal exponents m such that the fractional part of (10/9)^m obtains a maximum (when starting with m=1).

from itertools import islice
from oeis_sequences.OEISsequences import A153695_gen
print(list(islice(A153695_gen(),10)))
>> [1, 2, 3, 4, 5, 6, 13, 17, 413, 555]

Numbers n such that n³ has one or more occurrences of exactly nine different digits.

from oeis_sequences.OEISsequences import A235811_gen 
print(list(islice(A235811_gen(startvalue=1475),10))) # print first 10 terms >= 1475
>> [1475, 1484, 1531, 1706, 1721, 1733, 1818, 1844, 1895, 1903]