Math::NumSeq::LuckyNumbers -- sieved out multiples by the sequence itself


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


This is the so-called "Lucky" numbers obtained by sieving out multiples taken from the sequence itself

    starting i=1
    1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, ...

The sieve begins with the odd numbers


Then sieve[2]=3 from the sequence means remove every third number, counting from the start, so remove 5,11,17, etc to leave


Then the next value sieve[3]=7 means remove every seventh number, so 19 etc, to leave


Then sieve[4]=9 means remove every ninth from what remains, and so on. In each case the removals count from the start of the values which remain at that stage.

It can be shown the values grow at roughly the same rate as the primes, i =~ value/log(value).


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

$seq = Math::NumSeq::LuckyNumbers->new ()

Create and return a new sequence object.

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

Return an estimate of the i corresponding to $value. It can be shown that values grow roughly at the same rate as the primes,

    i ~= value/log(value)

So value_to_i_estimate() returns $value/log($value).


Math::NumSeq, Math::NumSeq::ReRound, Math::NumSeq::ReReplace



Copyright 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.

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