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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.

%I A364405 #19 Aug 26 2023 02:52:53
%S A364405 12,16,20,24,38,46,48,50,54,56,66,70,78,81,84,88,91,96,98,99,100,104,
%T A364405 116,122,126,130,132,135,138,141,148,150,155,156,161,162,164,166,168,
%U A364405 176,180,182,193,196,200,201,204,205,210,212,214,218,220,228,232,234,236
%N 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.
%C A364405 Positive numbers not in A084242.
%o A364405 (Ruby)
%o A364405 def gcdsteps(k, m)
%o A364405   k.zero? ? 0 : 1 + gcdsteps(m % k, k)
%o A364405 end
%o A364405 flags = [nil, *1..2000]
%o A364405 (1..flags.length).each do |m|
%o A364405   scores = []
%o A364405   (1..m).each do |k|
%o A364405     scores << [gcdsteps(k, m), k]
%o A364405   end
%o A364405   flags[scores.sort_by { |n| -n[0] }.first[1]] = nil
%o A364405 end
%o A364405 puts flags[1..flags.length / 2].compact
%Y A364405 Cf. A084242, A051010.
%K A364405 nonn
%O A364405 1,1
%A A364405 _John Metcalf_, Jul 22 2023