NAME

Math::NumSeq::SevenSegments -- count of segments to display by 7-segment LED

SYNOPSIS

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

DESCRIPTION

This sequence is how many segments are lit to display i in 7-segment LEDs

    i     = 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
    value = 6, 2, 5, 5, 4, 5, 6, 3, 7, 5, 8, 4, 7, 7, 6, 7, 8 ...
            (A277116)

The segments for each digit are

     ---                 ---       ---
    |   |         |         |         |     |   |
                         ---       ---       ---
    |   |         |     |             |         |
     ---                 ---       ---

     ---       ---       ---       ---       ---
    |         |             |     |   |     |   |
     ---       ---                 ---       ---
        |     |   |         |     |   |         |
     ---       ---                 ---

i=0 is considered to require one 0 digit, as is usual for a human display. (Although many mathematical things are much better consistently omitting all high 0 digits so that 0 is no digits.)

Option six => $integer is how many segments for digit 6. Occasionally it may be shown without the top, so 5 segments (instead of 6). This tends to look like a "b", and certainly would not be used when wanting an actual b too (for hexadecimal or text).

    |
     ---         six => 5   segments, (no top)
    |   |
     ---

Option seven => $integer is how many segments for digit 7. Sometimes 7 has a top-left "serif",

     ---
    |   |        seven => 4   segments (with top left)

        |

Option nine => $integer is how many segments for digit 9. Often 9 has a bottom segment.

     ---
    |   |        nine  => 6   segments (with bottom segment)
     ---
        |
     ---

It might have been more consistent if the default had been 6 and 9 both 6 segments, but the options allow any combination.

The total segments to display i is similar to Math::NumSeq::DigitSum, but with digits mapped through a table of segment counts 0->6, 1->2, 2->5, etc.

FUNCTIONS

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

$seq = Math::NumSeq::SevenSegments->new ()
$seq = Math::NumSeq::SevenSegments->new (key => value, ...)

Create and return a new sequence object. The optional key/value parameters are the number of segments lit for digits 6, 7, or 9,

    six   => $integer, default 6
    seven => $integer, default 3
    nine  => $integer, default

Random Access

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

Return the number of segments to display $i in 7-segment LEDs.

$i = $seq->i_start ()

Return 0, the first term in the sequence being at i=0.

OEIS

Entries in Sloane's Online Encyclopedia of Integer Sequences related to this sequence include

    A277116      default
    A074458      seven => 4              (but it just 0..9)
    A010371      seven => 4, nine => 6
    A006942                  nine => 6
    A063720      six => 5

SEE ALSO

Math::NumSeq, Math::NumSeq::DigitSum, Math::NumSeq::DigitLength, Math::NumSeq::AlphabeticalLength

Tk::SevenSegmentDisplay

HOME PAGE

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

LICENSE

Copyright 2012, 2015, 2020 Kevin Ryde

Math-NumSeq-Alpha 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-Alpha 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-Alpha. If not, see http://www.gnu.org/licenses/.