A364405 Numbers k such that k is never the smallest number which requires the maximum number of steps for the Euclidean algorithm for computing gcd(k,m) for any m > k.

12, 16, 20, 24, 38, 46, 48, 50, 54, 56, 66, 70, 78, 81, 84, 88, 91, 96, 98, 99, 100, 104, 116, 122, 126, 130, 132, 135, 138, 141, 148, 150, 155, 156, 161, 162, 164, 166, 168, 176, 180, 182, 193, 196, 200, 201, 204, 205, 210, 212, 214, 218, 220, 228, 232, 234, 236

Offset: 1

Author

John Metcalf, Jul 22 2023

Keywords

• nonn

Comments

Positive numbers not in A084242.

Crossrefs

Cf. A084242, A051010.

Programs

Ruby

def gcdsteps(k, m)
  k.zero? ? 0 : 1 + gcdsteps(m % k, k)
end
flags = [nil, *1..2000]
(1..flags.length).each do |m|
  scores = []
  (1..m).each do |k|
    scores << [gcdsteps(k, m), k]
  end
  flags[scores.sort_by { |n| -n[0] }.first[1]] = nil
end
puts flags[1..flags.length / 2].compact