NAME
Math::Aronson  generate values of Aronson's sequence
SYNOPSIS
use Math::Aronson;
my $aronson = Math::Aronson>new;
print $aronson>next,"\n"; # 1
print $aronson>next,"\n"; # 4
print $aronson>next,"\n"; # 11
DESCRIPTION
This is a bit of fun generating Aronson's sequence of numbers formed by selfreferential occurrences of the letter T in numbers written out in words.
T is the first, fourth, eleventh, sixteenth, ...
^ ^ ^ ^ ^ ^ ^
1 4 11 16 24 29 33 < sequence
In the initial string "T is the", the letter T is the first and fourth letters, so those words are appended to make "T is the first, fourth". Those words have further Ts at 11 and 16, so those numbers are appended, and so on.
Spaces and punctuation are ignored. Accents like acutes are stripped for letter matching. The without_conjunctions
option can ignore "and" or "et" too.
Termination
It's possible for the English sequence to end since there's no T in some numbers, but there doesn't seem enough of those, or the sequence doesn't fall on enough of them. (Is that proven?)
But for example using letter "F" instead gives a finite sequence,
$it = Math::Aronson>new (letter => 'F'); # 1, 7 only
This is "F is the first, seventh" giving 1, 7 but ends there as there's no more "F"s in "seventh". See examples/terminate.pl to run thorough which letters seem to terminate or not.
OEIS
Sloane's OnLine Encyclopedia of Integer Sequences has entries for Aronson's sequence and some variations
http://oeis.org/A005224
A005224 without_conjunctions=>1
A055508 letter=>'H', without_conjunctions=>1
A049525 letter=>'I', without_conjunctions=>1
A081023 lying=>1, without_conjunctions=>1
A072886 lying=>1, initial_string=>"S ain't the"
A080520 lang=>'fr'
A081024 complement of lying A081023
A072887 complement of lying "S ain't" A072886
A072421 Latin P
A072422 Latin N
A072423 Latin T
The English sequences are without conjunctions, hence for example
# sequence A005224
$it = Math::Aronson>new (without_conjunctions => 1);
The "lying" versions A081023 and A072886 are presumably the same, but the sample values don't go far enough to see a difference.
FUNCTIONS
The sequence is an infinite recurrence (or may be) so is generated in iterator style from an object created with various options.
Constructor
$it = Math::Aronson>new (key => value, ...)

Create and return a new Aronson sequence object. The following optional key/value parameters affect the sequence.
lang => $string
(default "en")
The language to use for the sequence. "en" and "fr" have defaults for the options below. Other languages can be used if you have the
Lingua::Any::Numbers
module. initial_string => $str

The initial string for the sequence. The default is
English "T is the" French "E est la"
For other languages there's no default yet and an
initial_string
must be given. letter => $str

The letter to look for in the words. The default is the first letter of
initial_string
.When a
letter
is given the defaultinitial_string
follows that, so "X is the" or "X est la".$it = Math::Aronson>new (letter => 'H'); # is 1, 5, 16, 25, ... # per "H is the first, fifth, ..."
letter
andinitial_string
can be given together to use a letter not at the start of theinitial_string
. For example,$it = Math::Aronson>new (letter => 'T', initial_string => "I think T is"); # is 2, 7, 21, 23, ... # per "I think T is second, seventh, twentyfirst, ..."
without_conjunctions => $boolean
(default false)
Strip conjunctions, meaning "and"s, in the wording so for instance "one hundred and four" becomes "one hundred four". The default is leave unchanged whatever conjunctions
Lingua::Any::Numbers
(orordinal_func
below) gives. conjunctions_word => $string
(default "and" or "et")
The conjunction word to exclude if
without_conjunctions
is true. The default is "and" for English or "et" for French. For other languages there's no default. ordinal_func => $coderef
(default Lingua modules)
A function to call to turn a number into words. Each call is
$str = &$ordinal_func ($n);
The default is a call
to_ordinal($n,$lang)
ofLingua::Any::Numbers
, or for English and French a direct call toLingua::EN::Numbers
orLingua::FR::Numbers
. The string returned can be wide chars.An explicit
ordinal_func
can be used ifLingua::Any::Numbers
doesn't support a desired language, or perhaps for a bit of rewording.$it = Math::Aronson>new (ordinal_func => sub { my ($n) = @_; return something_made_from($n); });
There's nothing to select a gender from
Lingua::Any::Numbers
, as of version 0.30, so anordinal_func
might be used for instance to get feminine forms fromLingua::ES::Numbers
. lying => $bool
(default false)
A "lying" version of the sequence, where the positions described and returned are those without the target letter. So for example
T is the second, third, fifth, ... ^^ ^^ ^^^^^^ ^ 2,3, 5,6 7,8,9,10,11,12, 14, ... < sequence
Starting from "T is the", the first position is a T so "first" is not appended, but the second position is not a T so lie by giving "second", and similarly the third position, but the fourth is a T so it doesn't appear.
Operations
$n = $it>next

Return the next number in the sequence, being the next position of T (or whatever letter) in the text. The first position is 1.
If the end of the sequence has been reached then the return is an empty list (which means
undef
in scalar context). Because positions begin at 1 a loop can be simplywhile (my $n = $it>next) { ... }
IMPLEMENTATION NOTES
Accents are stripped using Unicode::Normalize
if available (Perl 5.8.0 and up), or a builtin Latin1 table as a fallback otherwise. The Latin1 suits Lingua::FR::Numbers
and probably most of the European numbers modules.
The Lingua modules and string processing means next
probably isn't particularly fast. It'd be possible to go numbersonly with the usual rules for ordinals as words but generating just the positions of the "T"s or whatever desired letter, but that doesn't seem worth the effort.
SEE ALSO
Lingua::EN::Numbers, Lingua::FR::Numbers, Lingua::Any::Numbers
HOME PAGE
http://user42.tuxfamily.org/matharonson/index.html
LICENSE
MathAronson is Copyright 2010, 2011, 2012, 2017, 2019 Kevin Ryde
MathAronson 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.
MathAronson 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 MathAronson. If not, see <http://www.gnu.org/licenses/>.