Math::NumSeq::HappyNumbers -- reaching 1 under repeated sum of squares of digits


 use Math::NumSeq::HappyNumbers;
 my $seq = Math::NumSeq::HappyNumbers->new;
 my ($i, $value) = $seq->next;


This sequence is the happy numbers which are the numbers eventually reaching 1 on repeatedly taking the sum of the squares of the digits.

    1, 7, 10, 13, 19, 23, ...
    starting i=1

For example 23 is a happy number because the sum of squares of its digits (ie. 2 and 3) is 2*2+3*3=13, then the same sum of squares again 1*1+3*3=10, then 1*1+0*0=1 reaches 1.

In decimal it can be shown that for a non-zero starting point this procedure always reaches either 1 or the cycle 4,16,37,58,89,145,42,20. The values which reach 1 are called happy numbers.

An optional radix parameter can select a base other than decimal. Base 2 and base 4 are not very interesting since for them every number except 0 is happy.


See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::HappyNumbers->new ()
$seq = Math::NumSeq::HappyNumbers->new (radix => $r)

Create and return a new sequence object.

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

Return true if $value is a happy number, meaning repeated sum of squares of its digits reaches 1.


Math::NumSeq, Math::NumSeq::HappySteps, Math::NumSeq::DigitSum



Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 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 <>.