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A379067 Smallest missing positive number after A377091(n) has been found.

%I A379067 #35 Apr 08 2025 23:11:40
%S A379067 1,2,3,3,3,4,5,6,6,6,7,8,9,9,9,9,9,9,9,9,9,9,10,11,12,14,14,14,14,14,
%T A379067 14,14,14,15,16,17,19,19,19,19,19,19,19,19,19,19,22,22,24,24,24,24,29,
%U A379067 29,29,29,29,29,29,29,29,29,29,29,33,34,35,36,37,38,39,40,41,42,42,42,42,42,42,42,42,42,43,44,45,46,47,48,49,50,51,51,51,51,51,51,51,51
%N A379067 Smallest missing positive number after A377091(n) has been found.
%C A379067 Conjecture: lim sup |a(n) - n/2|/sqrt(n) = 1/2 (see links). This would imply that after A377091(n) has been found, A377091 contains all numbers in the range [0,f(n)], where lim sup f(n) = (n-sqrt(n))/2. There is a corresponding conjecture for A379068. - _N. J. A. Sloane_ and _Paolo Xausa_, Feb 03 2025
%H A379067 N. J. A. Sloane, <a href="/A379067/b379067.txt">Table of n, a(n) for n = 0..10000</a>
%H A379067 N. J. A. Sloane, <a href="https://oeis.org/A379067/a379067.txt">Table of n, A379067(n), A379068(n) for n = 0..999995</a>.
%H A379067 Paolo Xausa, <a href="/A379067/a379067_2.png">Scatterplot of |a(n) - n/2|/sqrt(n) for 1 <= n <= 10^6</a>. The orange line is y = 1/2.
%H A379067 Paolo Xausa, <a href="/A379067/a379067_3.png">Scatterplot of |a(n) - n/2|/sqrt(n) for 900000 <= n <= 10^6</a>. The orange line is y = 1/2.
%t A379067 (* A377091list is defined at A377091 *)
%t A379067 Module[{s, a}, s[_] := False; FoldList[(s[#2] = True; a = #; While[s[a], a++]; a) &, 1, Rest[A377091list[100]]]] (* _Paolo Xausa_, Apr 08 2025 *)
%Y A379067 Cf. A377091, A379068.
%K A379067 nonn
%O A379067 0,2
%A A379067 _N. J. A. Sloane_, Dec 28 2024