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A367935
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Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors of a(n) + a(n + 1) is a prime.
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1
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1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 12, 11, 13, 14, 15, 16, 18, 19, 17, 20, 21, 22, 25, 23, 24, 26, 27, 31, 28, 30, 29, 32, 35, 33, 34, 37, 36, 43, 38, 41, 39, 40, 42, 46, 50, 47, 49, 48, 52, 44, 45, 51, 56, 53, 54, 55, 58, 60, 61, 57, 59, 62, 63, 64, 67, 69, 68, 71, 65, 66, 70, 72, 77, 74, 75, 76, 73, 78, 79, 81, 82
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OFFSET
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1,2
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COMMENTS
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The sum of the distinct prime factors of n is sometimes called sopf(n).
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LINKS
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EXAMPLE
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a(1) + a(2) = 1 + 2 = 3 whose sopf is 3, a prime number;
a(2) + a(3) = 2 + 3 = 5 whose sopf is 5, a prime number;
a(7) + a(8) = 7 + 9 = 16 whose sopf is 2, a prime number;
a(8) + a(9) = 9 + 8 = 17 whose sopf is 17, a prime number;
a(9) + a(10) = 8 + 10 = 18 whose sopf is 2 + 3 = 5, a prime number; etc.
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||!PrimeQ@Total[First/@FactorInteger[k+a[n-1]]], k++]; k); Array[a, 81]
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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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