1Math::NumSeq::HappyStepUss(e3r)Contributed Perl DocumentMaattiho:n:NumSeq::HappySteps(3)
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6 Math::NumSeq::HappySteps -- number of sum of squares of digits
7 iterations to reach a repeat
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10 use Math::NumSeq::HappySteps;
11 my $seq = Math::NumSeq::HappySteps->new (radix => 10);
12 my ($i, $value) = $seq->next;
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15 This is the number of iterations of the "HappyNumbers" style "sum of
16 squares of digits" is required to reach a repeat of a value seen
17 before, and therefore to establish whether a number is a happy number
18 or not.
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20 1, 9, 13, 8, 12, 17, 6, 13, 12, 2,
21 starting i=1
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23 For example i=10 is value 2 because 10->1->1 is 2 iterations to get to
24 a repeat (a repeat of 1). At i=1 itself the value is 1 since 1
25 iteration reaches 1 again which is itself the repeat. That count 1 at
26 i=1 is the minimum.
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28 Radix
29 An optional "radix" parameter selects a base other than decimal. In
30 binary "radix=>2" the digits are all either 0 or 1 so "sum of squares
31 of digits" is the same as a plain "sum of digits".
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33 In some bases there's longer cycles than others which a non-happy
34 number might fall into. For example base 20 has a cycle
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36 10 -> 100 -> 25 -> 26 -> ... -> 61 -> 10
37 total 26 elements
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39 When a non-happy falls into such a cycle its "HappySteps" count here is
40 at least 26 (or whatever amount) to reach a repeat.
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43 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
44 classes.
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46 "$seq = Math::NumSeq::HappySteps->new ()"
47 "$seq = Math::NumSeq::HappySteps->new (radix => $r)"
48 Create and return a new sequence object.
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50 Random Access
51 "$value = $seq->ith($i)"
52 Return the number of iterations starting from $i required to reach
53 a repeat.
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56 Math::NumSeq, Math::NumSeq::HappyNumbers, Math::NumSeq::DigitSum
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59 <http://user42.tuxfamily.org/math-numseq/index.html>
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62 Copyright 2011, 2012, 2013, 2014, 2016 Kevin Ryde
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64 Math-NumSeq is free software; you can redistribute it and/or modify it
65 under the terms of the GNU General Public License as published by the
66 Free Software Foundation; either version 3, or (at your option) any
67 later version.
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69 Math-NumSeq is distributed in the hope that it will be useful, but
70 WITHOUT ANY WARRANTY; without even the implied warranty of
71 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
72 General Public License for more details.
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74 You should have received a copy of the GNU General Public License along
75 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
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79perl v5.30.0 2019-08-05 Math::NumSeq::HappySteps(3)