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A329406
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Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any four consecutive terms there is exactly one prime sum.
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12
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1, 2, 7, 8, 4, 14, 11, 5, 10, 3, 15, 6, 13, 9, 12, 16, 17, 18, 19, 21, 27, 24, 22, 20, 25, 26, 23, 28, 30, 32, 33, 31, 29, 34, 36, 35, 40, 41, 39, 37, 38, 42, 43, 45, 44, 47, 46, 50, 48, 49, 56, 62, 52, 53, 54, 58, 57, 51, 59, 68, 55, 60, 63, 64, 61, 65, 67, 74, 69, 72, 70, 66, 71, 75, 77, 76, 78
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OFFSET
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1,2
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COMMENTS
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For all n >= 1, there is exactly one prime in {a(n+i) + a(n+j), 0 <= i < j <= 3}. See A329450, A329452 onwards for variants for nonnegative integers. - M. F. Hasler, Nov 14 2019
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LINKS
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EXAMPLE
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a(1) = 1 by minimality.
a(2) = 2 as 2 is the smallest available integer not leading to a contradiction. Note that as 1 + 2 = 3 we already have our prime sum.
a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce one prime sum too many.
a(5) = 4 as a(5) = 3 would produce two primes instead of one (3 + 2 = 5 and 3 + 8 = 11); with a(5) = 4 we have the single prime sum we need among the last 4 integers {2,7,8,4}: 11 = 4 + 7.
And so on.
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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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