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A338141
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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.
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2
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2, 3, 5, 5, 7, 17, 11, 13, 31, 17, 19, 47, 23, 41, 47, 29, 31, 73, 59, 37, 67, 41, 43, 71, 47, 79, 83, 53, 89, 131, 59, 61, 103, 107, 67, 113, 71, 73, 173, 131, 79, 127, 83, 137, 149, 89, 149, 149, 163, 97, 163, 101, 103, 241, 107, 109, 257, 113, 191, 197, 179
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OFFSET
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1,1
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COMMENTS
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In other words, we partition the natural numbers into finite subsets summing to prime numbers.
Every prime number appears at least once in the sequence.
See A338240 for the corresponding {r_n}.
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LINKS
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EXAMPLE
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The first terms, alongside the corresponding sets r_n, are:
n a(n) r_n
-- ---- ------------
1 2 {2}
2 3 {3}
3 5 {1, 4}
4 5 {5}
5 7 {7}
6 17 {8, 9}
7 11 {11}
8 13 {13}
9 31 {6, 10, 15}
10 17 {17}
11 19 {19}
12 47 {12, 14, 21}
13 23 {23}
14 41 {16, 25}
15 47 {20, 27}
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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