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%I #33 Feb 09 2020 15:58:09
%S 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,
%T 22,33,24,27,28,36,29,34,35,40,31,41,37,44,38,43,39,42,45,46,47,48,49,
%U 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
%N Among the pairwise sums of any five consecutive terms there is exactly one prime sum; lexicographically earliest such sequence of distinct positive numbers.
%H Jean-Marc Falcoz, <a href="/A329407/b329407.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 our prime sum.
%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) = 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.
%e And so on.
%Y Cf. A329333 (3 consecutive terms, exactly 1 prime sum).
%Y Cf. A329405: no prime among the pairwise sums of 3 consecutive terms.
%Y Cf. A329406 .. A329410: exactly 1 prime sum using 4, ..., 10 consecutive terms.
%Y Cf. A329411 .. A329416: exactly 2 prime sums using 3, ..., 10 consecutive terms.
%Y See also A329450, A329452 onwards for "nonnegative" variants.
%K nonn
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 13 2019
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