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A329409
Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any seven consecutive terms there is exactly one prime sum.
2
1, 2, 7, 8, 13, 14, 19, 36, 20, 6, 26, 4, 16, 49, 28, 29, 23, 5, 9, 11, 17, 10, 15, 25, 35, 3, 39, 30, 24, 21, 27, 31, 18, 33, 12, 37, 45, 32, 40, 48, 38, 50, 42, 43, 22, 46, 34, 44, 52, 41, 53, 47, 58, 64, 57, 51, 59, 61, 60, 54, 63, 65, 56, 55, 69, 67, 66, 77, 68, 75, 78, 70, 72, 84, 62, 80, 81, 74, 71
OFFSET
1,2
LINKS
EXAMPLE
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 a prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least a 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) = 15, 16, 17 or 18 would produce at least a prime sum too many.
a(8) = 36 is the smallest available integer that produces the single prime sum we need among the last 7 integers {2, 7, 8, 13, 14, 19, 36}, which is 43 = 36 + 7.
And so on.
CROSSREFS
Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.
Sequence in context: A047239 A329410 A246389 * A231625 A032927 A004717
KEYWORD
nonn
AUTHOR
STATUS
approved