sidef-scripts/Math/irregular_triangle_of_n_AND_k.sf

#!/usr/bin/ruby

# Generate a nice sequence of numbers, generated by an irragular triangle, based on the logical binary equation:
#   n AND k = k, where k are values in the range [1, n]

# See also:
#   https://oeis.org/A038573
#   https://oeis.org/A335063
#   https://oeis.org/A048967

# Reading these irregular triangles by rows in a flat list,
# and plotting the list, generates the Sierpiński triangle.

# See also:
#   https://en.wikipedia.org/wiki/Sierpiński_triangle

say ":: Irregular triangle of numbers n such that n AND k = k:\n"

var seq_lens = []
var seq_sums = []

for n in (1..20) {
    var arr = (1..n -> grep {|k| n&k == k })
    seq_lens << arr.len
    seq_sums << arr.sum
    say ("#{'%2d' % n}: ", arr)
}

say ''

say "Lens: #{seq_lens}"
say "Sums: #{seq_sums}"

say "\n#{'-' * 80}\n"

say ":: Irregular triangle of numbers n such that n AND k != k:\n"

var seq_neg_lens = []
var seq_neg_sums = []

for n in (1..20) {
    var arr = (1..n -> grep {|k| n&k != k })
    seq_neg_lens << arr.len
    seq_neg_sums << arr.sum
    say ("#{'%2d' % n}: ", arr)
}

say ''

say "Lens: #{seq_neg_lens}"
say "Sums: #{seq_neg_sums}"

__END__
:: Irregular triangle of numbers n such that n AND k = k:

 1: [1]
 2: [2]
 3: [1, 2, 3]
 4: [4]
 5: [1, 4, 5]
 6: [2, 4, 6]
 7: [1, 2, 3, 4, 5, 6, 7]
 8: [8]
 9: [1, 8, 9]
10: [2, 8, 10]
11: [1, 2, 3, 8, 9, 10, 11]
12: [4, 8, 12]
13: [1, 4, 5, 8, 9, 12, 13]
14: [2, 4, 6, 8, 10, 12, 14]
15: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
16: [16]
17: [1, 16, 17]
18: [2, 16, 18]
19: [1, 2, 3, 16, 17, 18, 19]
20: [4, 16, 20]

Lens: [1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3]
Sums: [1, 2, 6, 4, 10, 12, 28, 8, 18, 20, 44, 24, 52, 56, 120, 16, 34, 36, 76, 40]

--------------------------------------------------------------------------------

:: Irregular triangle of numbers n such that n AND k != k:

 1: []
 2: [1]
 3: []
 4: [1, 2, 3]
 5: [2, 3]
 6: [1, 3, 5]
 7: []
 8: [1, 2, 3, 4, 5, 6, 7]
 9: [2, 3, 4, 5, 6, 7]
10: [1, 3, 4, 5, 6, 7, 9]
11: [4, 5, 6, 7]
12: [1, 2, 3, 5, 6, 7, 9, 10, 11]
13: [2, 3, 6, 7, 10, 11]
14: [1, 3, 5, 7, 9, 11, 13]
15: []
16: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
17: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
18: [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17]
19: [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
20: [1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19]

Lens: [0, 1, 0, 3, 2, 3, 0, 7, 6, 7, 4, 9, 6, 7, 0, 15, 14, 15, 12, 17]
Sums: [0, 1, 0, 6, 5, 9, 0, 28, 27, 35, 22, 54, 39, 49, 0, 120, 119, 135, 114, 170]