Inventory sequence

Inventory sequence is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

To build the inventory sequence, first take inventory of what numbers are already in the sequence, then, starting with 0 add the count of each number in turn to the end of the sequence. When you reach a number that has a count of 0, stop, add the 0 to the end of the sequence, and then restart the inventory from 0.

E.G.

Start taking inventory; how many 0s are there? 0. Add a 0 to the end of the sequence and restart the inventory. (0)

How many 0s are there? 1. Add a 1 to the end of the sequence. How many 1s are there? 1. Add a 1 to the end of the sequence. How many 2s are there? 0. Add a 0 to the end of the sequence and restart the inventory. (0 1 1 0)

and so on.

Task

• Find and display the first 100 elements of the sequence.
• Find and display the position and value of the first element greater than or equal to 1000.

Stretch

• Find and display the position and value of the first element greater than or equal to 2000, 3000 ... 10,000.
• Plot a graph of the first 10,000 elements of the sequence.

See also

• OEIS:A342585 - Inventory sequence
• Numberphile: The inventory sequence

Python

''' rosettacode.org/wiki/Inventory_sequence '''
from collections import Counter
from matplotlib.pyplot import plot

def inventory_sequence(terms):
    ''' From the code by Branicky at oeis.org/A342585 '''
    num, alst, inventory = 0, [0], Counter([0])
    for n in range(2, terms+1):
        c = inventory[num]
        num = 0 if c == 0 else num + 1
        alst.append(c)
        inventory.update([c])
    return alst

biglist = inventory_sequence(201_790)
thresholds = [1000 * j for j in range(1, 11)]

for i, k in enumerate(biglist):
    if i < 100:
        print(f'{k:<4}', end='\n' if (i + 1) % 20 == 0 else '')
    elif k >= thresholds[0]:
        print(f'\nFirst element >= {thresholds.pop(0):5}: {k:5} in position {i:6}')
        if len(thresholds) == 0:
               break

plot(biglist[:10_000], linewidth=0.3)

Output:

0   1   1   0   2   2   2   0   3   2   4   1   1   0   4   4   4   1   4   0   
5   5   4   1   6   2   1   0   6   7   5   1   6   3   3   1   0   7   9   5   
3   6   4   4   2   0   8   9   6   4   9   4   5   2   1   3   0   9   10  7   
5   10  6   6   3   1   4   2   0   10  11  8   6   11  6   9   3   2   5   3   
2   0   11  11  10  8   11  7   9   4   3   6   4   5   0   12  11  10  9   13  

First element >=  1000:  1001 in position  24255

First element >=  2000:  2009 in position  43301

First element >=  3000:  3001 in position  61708

First element >=  4000:  4003 in position  81456

First element >=  5000:  5021 in position  98704

First element >=  6000:  6009 in position 121342

First element >=  7000:  7035 in position 151756

First element >=  8000:  8036 in position 168804

First element >=  9000:  9014 in position 184428

First element >= 10000: 10007 in position 201788

Raku

use Lingua::EN::Numbers;

my ($i, %i) = 0;

my @inventory = (^∞).map: {
    my $count = %i{$i} // 0;
    $i = $count ?? $i+1 !! 0;
    ++%i{$count};
    $count
}

say "Inventory sequence, first 100 elements:\n" ~
  @inventory[^100].batch(20)».fmt("%2d").join: "\n";

say '';

for (1..10).map: * × 1000 {
    my $k = @inventory.first: * >= $_, :k;
    printf "First element >= %6s is %6s in position: %s\n",
      .&comma, @inventory[$k].&comma, comma $k;
}


use SVG;
use SVG::Plot;

my @x = ^10000;

'Inventory-raku.svg'.IO.spurt:
 SVG.serialize: SVG::Plot.new(
    background  => 'white',
    width       => 1000,
    height      => 600,
    plot-width  => 950,
    plot-height => 550,
    x           => @x,
    values      => [@inventory[@x],],
    title       => "Inventory Sequence - First {+@x} values (zero indexed)",
).plot: :lines;

Output:

Inventory sequence, first 100 elements:
 0  1  1  0  2  2  2  0  3  2  4  1  1  0  4  4  4  1  4  0
 5  5  4  1  6  2  1  0  6  7  5  1  6  3  3  1  0  7  9  5
 3  6  4  4  2  0  8  9  6  4  9  4  5  2  1  3  0  9 10  7
 5 10  6  6  3  1  4  2  0 10 11  8  6 11  6  9  3  2  5  3
 2  0 11 11 10  8 11  7  9  4  3  6  4  5  0 12 11 10  9 13

First element >=  1,000 is  1,001 in position: 24,255
First element >=  2,000 is  2,009 in position: 43,301
First element >=  3,000 is  3,001 in position: 61,708
First element >=  4,000 is  4,003 in position: 81,456
First element >=  5,000 is  5,021 in position: 98,704
First element >=  6,000 is  6,009 in position: 121,342
First element >=  7,000 is  7,035 in position: 151,756
First element >=  8,000 is  8,036 in position: 168,804
First element >=  9,000 is  9,014 in position: 184,428
First element >= 10,000 is 10,007 in position: 201,788

converted to a .png to reduce size for display here: