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%I #14 Oct 18 2020 16:48:25
%S 2,3,5,5,7,17,11,13,31,17,19,47,23,41,47,29,31,73,59,37,67,41,43,71,
%T 47,79,83,53,89,131,59,61,103,107,67,113,71,73,173,131,79,127,83,137,
%U 149,89,149,149,163,97,163,101,103,241,107,109,257,113,191,197,179
%N Let R_1 = {1, 2, ...}; for any n > 0, let r_n be the colexicographically earliest finite subset of R_n summing to a prime number, say p; a(n) = p and R_{n+1} = R_n \ r_n.
%C In other words, we partition the natural numbers into finite subsets summing to prime numbers.
%C Every prime number appears at least once in the sequence.
%C See A338240 for the corresponding {r_n}.
%H Rémy Sigrist, <a href="/A338141/b338141.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A338141/a338141.png">Colored scatterplot of the first 100000 terms</a> (where the color is function of the number of elements of r_n)
%H Rémy Sigrist, <a href="/A338141/a338141.gp.txt">PARI program for A338141</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lexicographic_order#Colexicographic_order">Colexicographic order</a>
%e The first terms, alongside the corresponding sets r_n, are:
%e n a(n) r_n
%e -- ---- ------------
%e 1 2 {2}
%e 2 3 {3}
%e 3 5 {1, 4}
%e 4 5 {5}
%e 5 7 {7}
%e 6 17 {8, 9}
%e 7 11 {11}
%e 8 13 {13}
%e 9 31 {6, 10, 15}
%e 10 17 {17}
%e 11 19 {19}
%e 12 47 {12, 14, 21}
%e 13 23 {23}
%e 14 41 {16, 25}
%e 15 47 {20, 27}
%o (PARI) See Links section.
%Y Cf. A338240.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Oct 12 2020
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