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A379053 Lexicographically earliest infinite sequence of distinct positive numbers with the property that n is a member of the sequence iff a(n) is not a prime.

%I A379053 #19 Dec 18 2024 09:22:48
%S A379053 1,3,4,6,7,8,9,10,12,14,13,15,16,18,20,21,19,22,24,25,26,27,28,30,32,
%T A379053 33,34,35,23,36,37,38,39,40,42,44,45,46,48,49,43,50,51,52,54,55,53,56,
%U A379053 57,58,60,62,63,64,65,66,68,69,61,70,72,74,75,76,77,78,71
%N A379053 Lexicographically earliest infinite sequence of distinct positive numbers with the property that n is a member of the sequence iff a(n) is not a prime.
%C A379053 The sequence tells you exactly which terms of the sequence are either 1 or composite.
%C A379053 See the Comments in A379051 for further information.
%H A379053 Michael De Vlieger, <a href="/A379053/b379053.txt">Table of n, a(n) for n = 1..65536</a> [Terms 1 to 10000 from Scott R. Shannon]
%F A379053 When sorted, this appears to be the complement of [2, 5, 11, 17, 29, and prime(2*t+1), t >= 35]. - _Scott R. Shannon_, Dec 18 2024
%t A379053 nn = 120; u = 3; v = {}; w = {}; c = 4;
%t A379053 {1}~Join~Reap[Do[
%t A379053   If[MemberQ[w, n],
%t A379053     k = c; w = DeleteCases[w, n],
%t A379053     m = Min[{c, u, v}]; If[And[CompositeQ[m], n < m],
%t A379053       AppendTo[v, n]];
%t A379053       If[Length[v] > 0,
%t A379053         If[v[[1]] == m,
%t A379053         v = Rest[v]]]; k = m];
%t A379053     AppendTo[w, k]; If[k == c, c++; While[PrimeQ[c], c++]]; Sow[k];
%t A379053 If[n + 1 >= u, u++; While[CompositeQ[u], u++]], {n, 2, nn}] ][[-1, 1]] (* _Michael De Vlieger_, Dec 17 2024 *)
%Y A379053 Cf. A079000, A079253, A079254, A079313, A080032, A085925, A099797, A099798, A121053, A334067, A377901, A379051.
%K A379053 nonn
%O A379053 1,2
%A A379053 _N. J. A. Sloane_, Dec 17 2024
%E A379053 More terms from _Michael De Vlieger_, Dec 17 2024