Kevin Ryde > Math-NumSeq-65 > Math::NumSeq::JugglerSteps

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Module Version: 65   Source   Latest Release: Math-NumSeq-69

# NAME

Math::NumSeq::JugglerSteps -- steps in the juggler sqrt sequence

# SYNOPSIS

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

# DESCRIPTION

This is the number of steps it takes to reach 1 by the Juggler sqrt sequence,

```    n ->  /  floor(n^(1/2))      if n even
\  floor(n^(3/2))      if n odd```

So sqrt if n even, or sqrt(n^3) if n odd, each rounded downwards. For example i=17 goes 17 -> sqrt(17^3)=70 -> sqrt(70)=8 -> sqrt(8)=2 -> sqrt(2)=1, for a count of 4 steps.

```    0, 1, 6, 2, 5, 2, 4, 2, 7, 7, 4, 7, 4, 7, 6, 3, 4, 3, 9, 3, ...
starting i=1```

The intermediate values in the calculation can become quite large and `Math::BigInt` is used if necessary. There's some secret experimental caching in a temporary file, for a small speedup.

# FUNCTIONS

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

`\$seq = Math::NumSeq::JugglerSteps->new ()`
`\$seq = Math::NumSeq::JugglerSteps->new (step_type => 'both', juggler_type => '1/2-3/2')`

Create and return a new sequence object.

The optional `step_type` parameter (a string) selects between

```    "up"      upward steps sqrt(n^3)
"down"    downward steps sqrt(n)
"both"    both up and down, which is the default```

The optional `juggler_type` parameter (a string) selects among variations on the powering

```                  n even        n odd
"1/2-3/2"    sqrt(n)   and sqrt(n^3)
"2/3-3/2"    cbrt(n^2) and sqrt(n^3)
"3/4-4/3"    n^(3/4)   and n^(4/3)```

## Random Access

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

Return the number of steps to take `\$i` down to 1.

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

Return true if `\$value` occurs as a step count. This is simply `\$value >= 0`.

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

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/>.

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