and 1 contributors

# NAME

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

# SYNOPSIS

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

# DESCRIPTION

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, ...``

# FUNCTIONS

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`.

# HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

# LICENSE

Copyright 2010, 2011, 2012, 2013 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 <http://www.gnu.org/licenses/>.