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A338141
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.
2
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
OFFSET
1,1
COMMENTS
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}.
LINKS
Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the number of elements of r_n)
EXAMPLE
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}
PROG
(PARI) See Links section.
CROSSREFS
Cf. A338240.
Sequence in context: A302445 A094749 A096539 * A067364 A090547 A087308
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Oct 12 2020
STATUS
approved