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cpan:TOBS

# NAME

OEIS - Look up sequences on the On-Line Encyclopedia of Integer Sequences®

# SYNOPSIS

```use OEIS;

say OEIS::lookup 1, 1, * + * ... *;
#= OEIS A000045 «Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.»

say OEIS::lookup(1, 2, 4 ... ∞).mathematica.head;
#= Table[2^n, {n, 0, 50}]

# Notice that only some terms of the Seq are evaluated!
with OEIS::lookup-all(1, 1, * + * ... *).grep(* !~~ OEIS::easy).head {
say .gist;     #= OEIS A290689 «Number of transitive rooted trees with n nodes.»
say .sequence; #= [1 1 1 2 3 5 8 13 21 34 55 88 143 229 370 592 955 1527 2457 3929]
}
```

# DESCRIPTION

This module provides an interface to the On-Line Encyclopedia of Integer Sequences® (OEIS®), a web database of integer sequences. Stick an array or Seq into the `OEIS::lookup` routine and get back the most relevant result that OEIS finds, as an instance of OEIS::Entry. With the `:all` adverb or as the `OEIS::lookup-all` method, it returns a lazy Seq of all results. Sequences can also be looked up by their IDs. See below for details.

## sub fetch

```multi fetch (Int \$ID, :\$type = 'A')
multi fetch (Str \$ID where { … })
multi fetch (Seq \$seq)
multi fetch (*@partial-seq)
```

Searches for a sequence identified by

• its `Int \$ID` under the `\$type` namespace, e.g. the Fibonacci numbers are sequence 45 in type `A`, 692 in type `M` and 256 in type `N`,

• its `Str \$ID` already containing the `\$type`, again the Fibonacci numbers are "A000045", "M0692" or "N0256",

• a Seq generating the sequence,

• an array containing sequence elements

and returns all result pages in OEIS's internal text format as a lazy Seq.

This is a very low-level method. See OEIS::lookup for a more convenient interface.

## sub chop-records

```multi chop-records (Seq \pages)
multi chop-records (Str \$page)
```

Takes a single page in OEIS' internal format, or a Seq of them (the return value of OEIS::fetch), and returns a Seq of all OEIS records contained in them, as multiline strings.

You will only need this sub if you get pages from a source that isn't OEIS::fetch, e.g. from a cache on disk, or if you want the textual records instead of OEIS::Entry objects.

For a more convenient interface, see OEIS::lookup.

## sub lookup

```sub lookup (:\$all = False, |c)
```

This high-level sub calls OEIS::fetch with the captured arguments `|c`, followed by OEIS::chop-records and then creates for each record an OEIS::Entry object. Naturally, all search features of OEIS::fetch are supported.

By default only the first record is returned. This is the one that OEIS deems most relevant to the search. If the named argument `\$all` is True, all records are returned as a lazy Seq.

If no result was found, the Seq is empty. Note that a too general query leads to "too many results, please narrow search" error from the OEIS. For other possible errors, see X::OEIS.

## sub lookup-all

```sub lookup-all (|c)
```

This sub is equivalent to `lookup(:all, |c)`. It exists because when you write a Seq directly into the `lookup` call, the `:all` adverb is swallowed into the Seq by the comma operator, unless the Seq is parenthesized, which you may want to avoid having to do.