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A329407
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Among the pairwise sums of any five consecutive terms there is exactly one prime sum; lexicographically earliest such sequence of distinct positive numbers.
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1
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1, 2, 7, 8, 13, 12, 14, 4, 20, 21, 6, 18, 15, 10, 3, 17, 5, 11, 16, 25, 9, 19, 23, 30, 26, 32, 22, 33, 24, 27, 28, 36, 29, 34, 35, 40, 31, 41, 37, 44, 38, 43, 39, 42, 45, 46, 47, 48, 49, 68, 51, 57, 54, 53, 61, 58, 62, 50, 52, 59, 56, 60, 55, 67, 63, 65, 66, 69, 75, 77, 64, 71, 70, 72, 73, 76, 74, 80
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OFFSET
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1,2
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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 at least one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least one prime sum too many.
a(5) = 13 as a(5) = 3, 4, 5, 6, 9, 10, 11 or 12 would also produce at least one prime sum too many.
a(6) = 12 and we have the single prime sum we need among the last 5 integers {2,7,8,13,12}, which is 19 = 12 + 7.
And so on.
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CROSSREFS
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Cf. A329333 (3 consecutive terms, exactly 1 prime sum).
Cf. A329405: no prime among the pairwise sums of 3 consecutive terms.
Cf. A329406 .. A329410: exactly 1 prime sum using 4, ..., 10 consecutive terms.
Cf. A329411 .. A329416: exactly 2 prime sums using 3, ..., 10 consecutive terms.
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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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