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# NAME

Math::NumSeq::Pronic -- pronic numbers

# SYNOPSIS

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

# DESCRIPTION

The pronic numbers i*(i+1),

``````    0, 2, 6, 12, 20, 30, ...
starting i=0``````

These are twice the triangular numbers, and half way between the perfect squares.

# FUNCTIONS

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

`\$seq = Math::NumSeq::Pronic->new ()`

Create and return a new sequence object.

## Iterating

`\$seq->seek_to_i(\$i)`

Move the current sequence position to `\$i`. The next call to `next()` will return `\$i` and corresponding value.

`\$seq->seek_to_value(\$value)`

Move the current sequence position so that `next()` will give `\$value` on the next call, or if `\$value` is not a pronic number then the next pronic above `\$value`.

## Random Access

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

Return `\$i*(\$i+1)`.

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

Return true if `\$value` is a pronic number, ie. i*(i+1) for some i.

`\$i = \$seq->value_to_i_ceil(\$value)`
`\$i = \$seq->value_to_i_floor(\$value)`

Return the `\$i` index of `\$value`, rounding up or down if `\$value` is not a pronic number.

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

Return an estimate of the i corresponding to `\$value`. value=i*(i+1) is inverted by

``    \$i = int( (sqrt(4*\$value + 1) - 1)/2 )``