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A329410
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Among the pairwise sums of any ten consecutive terms there is exactly one prime sum: lexicographically earliest such sequence of distinct positive numbers.
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6
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1, 2, 7, 8, 13, 14, 19, 20, 25, 26, 108, 32, 37, 38, 44, 50, 10, 40, 12, 18, 28, 48, 105, 6, 4, 16, 24, 30, 36, 42, 54, 56, 9, 46, 22, 60, 66, 68, 72, 76, 78, 82, 93, 34, 52, 62, 43, 83, 92, 102, 23, 53, 3, 29, 31, 27, 33, 41, 15, 88, 5, 11, 17, 35, 45, 47, 55, 57, 21, 64, 51, 59, 61, 65, 39, 69, 71, 77, 79, 136, 49, 67, 63
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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 have already the prime sum we need.
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) = 14 as a(6) = 14 doesn't produce an extra prime sum - only composite sums.
a(7) = 19 as a(7) = 3, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17 or 18 would produce at least a prime sum too many.
a(8) = 20 as a(8) = 20 doesn't produce an extra prime sum - only composite sums.
a(9) = 25 as a(9) = 3, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 18, 21, 22, 23 or 24 would produce at least a prime sum too many.
a(10) = 26 as(10) = 26 doesn't produce an extra prime sum - only composite sums.
a(11) = 108 is the smallest available integer that produces the single prime sum we need among the last 10 integers {2,7,8,13,14,19,20,25,26,108}, which is 127 = 108 + 19.
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 .. A329409 (exactly 1 prime sum using 4, ..., 7 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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