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A225947
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Lexicographically least sequence of primes (including 1) that are sum-free.
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2
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1, 2, 5, 11, 23, 43, 47, 137, 157, 293, 439, 1163, 1201, 2339, 3529, 5867, 9391, 23623, 24659, 49477, 72953, 147083, 195511, 392059, 538001, 1052479, 1590467, 2520503, 4503007, 5041007, 14047027, 15637483, 28239989, 55404001, 115994933, 210773399
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OFFSET
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1,2
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COMMENTS
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A sum-free sequence has no term that is the sum of a subset of its previous terms. There are an infinite number of sequences that are subsets of {1} union primes and sum-free. This sequence is lexicographically the first.
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LINKS
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EXAMPLE
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a(8)=137 as 137 is the next prime after a(7)=47 that cannot be formed from distinct sums of a(1),...,a(7) (1,2,5,11,23,43,47).
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MATHEMATICA
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memberQ[n1_, k1_] := If[Select[IntegerPartitions[Prime[n1], Length[k1], k1], Sort@#==Union@# &]=={}, False, True]; k={1}; n=1; While[Length[k]<15, (If[!memberQ[n, k], k=Append[k, Prime[n]]]; n++)]; k
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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