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%I #11 Dec 03 2024 12:30:11
%S 1,4,5,8,9,11,12,15,16,19,22,23,26,27,29,30,33,34,37,40,41,44,45,48,
%T 51,52,55,56,58,59,62,63,66,69,70,73,74,76,77,80,81,84,85,87,88,91,92,
%U 95,98,99,102,103,105,106,109,110,113,116,117,120,121,124,127
%N First set of a unique partition of the positive integers into two sets whose distinct pair-sums avoid the Lucas numbers.
%C If x, y are distinct elements of this sequence then x+y is not a Lucas number.
%H K. Alladi, P. Erdös, and V. E. Hoggatt, Jr., <a href="https://doi.org/10.1016/0012-365X(78)90053-5">On additive partitions of integers</a>, Discrete Math. 22 (1978), 201-211.
%Y Cf. A000032, A378595.
%K nonn
%O 1,2
%A _Jeffrey Shallit_, Dec 01 2024