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%I #25 Nov 28 2019 11:01:22
%S 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,
%T 31,19,33,24,25,32,30,26,36,38,39,40,42,46,48,45,23,54,69,37,43,41,50,
%U 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
%N Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any six consecutive terms there is exactly one prime sum.
%H Jean-Marc Falcoz, <a href="/A329408/b329408.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 1 by minimality.
%e 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.
%e a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce at least one prime sum too many.
%e a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least one prime sum too many.
%e 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.
%e a(6) = 14 as a(6) = 14 doesn't produce an extra prime sum - only composite sums.
%e 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.
%e And so on.
%Y Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.
%K nonn
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 13 2019
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