Math::NumSeq -- number sequences


 # only a base class, use one of the actual classes such as
 use Math::NumSeq::Squares;
 my $seq = Math::NumSeq::Squares->new;
 my ($i, $value) = $seq->next;


This is a base class for number sequences. Sequence objects can iterate through the values, and some sequences have random access and predicate. It's a touch rough yet.

The idea is to generate things like squares or primes in a generic way. Some sequences, like squares, are so easy there's no need for this except for the genericness. Other sequences are trickier and an iterator is a good way to go through the values.


In the following "Foo" is one of the actual subclass names. The intention is that all modules Math::NumSeq::Something are sequence classes, and that supporting things are deeper, such as under Math::NumSeq::Something::Helper or Math::NumSeq::Base::SharedStuff.

$seq = Math::NumSeq::Foo->new (key=>value,...)

Create and return a new sequence object.

($i, $value) = $seq->next()

Return the next index and value in the sequence.


Rewind the sequence to its starting point.

$str = $seq->description()

A human-readable description of the sequence.

$value = $seq->values_min()
$value = $seq->values_max()

Return the minimum or maximum value taken by values in the sequence, or undef if unknown or infinity.

$ret = $seq->characteristic($key)

Return something if the sequence has a $key (a string) characteristic, or undef if not. This is intended as a loose set of expressing features or properties a sequence might have.

    digits      the radix (an integer), if sequence is digits
$str = $seq->oeis_anum()

Return the Online Encyclopedia of Integer Sequences A-number (a string) of $seq, or undef if not in the OEIS or not known. For example

    my $seq = Math::NumSeq::Squares->new;
    my $anum = $seq->oeis_anum;
    # gives $anum eq "A000290"

The web page for that is then

Sometimes the OEIS has duplicates, ie. two A-numbers which are the same sequence. $seq->oeis_anum() generally returns whichever is the primary one, at least for accidental duplication.

$aref = Math::NumSeq::Foo->parameter_info_array()
@list = Math::NumSeq::Foo->parameter_info_list()

Return an arrayref of list describing the parameters taken by a given class. This meant to help making widgets etc for user interaction in a GUI. Each element is a hashref

      name        =>    parameter key arg for new()
      description =>    human readable string
      type        =>    string "integer","boolean","enum" etc
      default     =>    value
      minimum     =>    number, or undef
      maximum     =>    number, or undef
      width       =>    integer, suggested display size
      choices     =>    for enum, an arrayref     

type is a string, one of


"filename" is separate from "string" since it might require subtly different handling to ensure it reaches Perl as a byte string, whereas a "string" type might in principle take Perl wide chars.

For "enum" the choices field is the possible values, such as

    { name => "flavour",
      type => "enum",
      choices => ["strawberry","chocolate"],

minimum and maximum are omitted if there's no hard limit on the parameter.

Optional Methods

The following methods are only implemented for some sequences, since it's sometimes difficult to generate an arbitrary numbered element etc. Check with $seq->can('ith') etc before using.

$value = $seq->ith($i)

Return the $i'th value in the sequence. Only some sequence classes implement this method.

$bool = $seq->pred($value)

Return true if $value occurs in the sequence. For example for the squares this would return true if $value is a square or false if not.


Math::NumSeq::Squares, Math::NumSeq::Cubes, Math::NumSeq::Pronic, Math::NumSeq::Triangular, Math::NumSeq::Polygonal, Math::NumSeq::Tetrahedral, Math::NumSeq::StarNumbers, Math::NumSeq::Even, Math::NumSeq::Odd, Math::NumSeq::All

Math::NumSeq::Primes, Math::NumSeq::TwinPrimes, Math::NumSeq::SophieGermainPrimes, Math::NumSeq::AlmostPrimes, Math::NumSeq::Emirps, Math::NumSeq::MobiusFunction, Math::NumSeq::PrimeFactorCount, Math::NumSeq::DivisorCount,

Math::NumSeq::Totient, Math::NumSeq::TotientCumulative, Math::NumSeq::TotientSteps, Math::NumSeq::TotientPerfect

Math::NumSeq::Factorials, Math::NumSeq::Primorials, Math::NumSeq::Fibonacci, Math::NumSeq::LucasNumbers, Math::NumSeq::Fibbinary, Math::NumSeq::Pell, Math::NumSeq::Tribonacci

Math::NumSeq::FractionDigits, Math::NumSeq::SqrtDigits

Math::NumSeq::DigitCount, Math::NumSeq::DigitLength, Math::NumSeq::DigitLengthCumulative, Math::NumSeq::DigitProduct, Math::NumSeq::DigitSum, Math::NumSeq::DigitSumModulo, Math::NumSeq::RadixWithoutDigit

Math::NumSeq::Palindromes, Math::NumSeq::Beastly, Math::NumSeq::Repdigits, Math::NumSeq::HarshadNumbers, Math::NumSeq::HappyNumbers

Math::NumSeq::CullenNumbers, Math::NumSeq::ProthNumbers, Math::NumSeq::WoodallNumbers Math::NumSeq::BaumSweet, Math::NumSeq::KlarnerRado Math::NumSeq::MephistoWaltz

Math::NumSeq::CollatzSteps, Math::NumSeq::JugglerSteps, Math::NumSeq::SternDiatomic, Math::NumSeq::NumAronson

Math::NumSeq::Kolakoski, Math::NumSeq::GolombSequence, Math::NumSeq::AsciiSelf

Math::NumSeq::Aronson, in the Math-Aronson dist

Math::Sequence and Math::Series, for symbolic recursive sequence definitions




Copyright 2010, 2011 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <>.