Math::NumSeq::DigitLengthCumulative -- total length in digits of numbers 1 to i


 use Math::NumSeq::DigitLengthCumulative;
 my $seq = Math::NumSeq::DigitLengthCumulative->new (radix => 10);
 my ($i, $value) = $seq->next;


The total length of numbers 0 to i, starting from i=0.

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, ...

"0" is taken to be a single digit, so the initial i=0 is total length 1. Then it's length 1 more for each of i=1 to i=9, then at i=10 length 2 more, etc.

The default is decimal, or the optional radix parameter can select another base. For example radix => 3 ternary,

    1, 2, 3, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, ...


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

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

Create and return a new sequence object.

Random Access

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

Return total length in digits of the numbers 0 to $i, inclusive.

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

Return true if $value occurs in the sequence.

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

Return the index i of $value or of the next cumulative total below $value.

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

Return an estimate of the i corresponding to $value.


Math::NumSeq, Math::NumSeq::DigitLength



Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 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 <>.