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 A329408 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any six consecutive terms there is exactly one prime sum. 1
 1, 2, 7, 8, 13, 14, 12, 20, 4, 22, 35, 10, 6, 16, 28, 29, 5, 34, 21, 15, 3, 11, 17, 18, 9, 27, 31, 19, 33, 24, 25, 32, 30, 26, 36, 38, 39, 40, 42, 46, 48, 45, 23, 54, 69, 37, 43, 41, 50, 44, 47, 49, 55, 61, 53, 62, 51, 57, 59, 63, 60, 58, 52, 64, 56, 77, 67, 65, 68, 66, 75, 78, 70, 74, 72, 80, 73, 71, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Jean-Marc Falcoz, Table of n, a(n) for n = 1..10000 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 already have 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) = 12 as 12 is the smallest available integer that produces the single prime sum we need among the last 6 integers {2,7,8,13,14,12}, which is 19 = 12 + 7. And so on. CROSSREFS Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards. Sequence in context: A129850 A037073 A329407 * A047239 A329410 A246389 Adjacent sequences:  A329405 A329406 A329407 * A329409 A329410 A329411 KEYWORD nonn AUTHOR Eric Angelini and Jean-Marc Falcoz, Nov 13 2019 STATUS approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)