cp's OEIS Frontend

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.

%I A329409 #29 Nov 28 2019 11:01:28
%S A329409 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,
%T A329409 39,30,24,21,27,31,18,33,12,37,45,32,40,48,38,50,42,43,22,46,34,44,52,
%U A329409 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
%N 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.
%H A329409 Jean-Marc Falcoz, <a href="/A329409/b329409.txt">Table of n, a(n) for n = 1..10000</a>
%e A329409 a(1) = 1 by minimality.
%e A329409 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.
%e A329409 a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce at least a prime sum too many.
%e A329409 a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least a prime sum too many.
%e A329409 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 A329409 a(6) = 14 as a(6) = 14 doesn't produce an extra prime sum - only composite sums.
%e A329409 a(7) = 19 as a(7) = 15, 16, 17 or 18 would produce at least a prime sum too many.
%e A329409 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.
%e A329409 And so on.
%Y A329409 Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.
%K A329409 nonn
%O A329409 1,2
%A A329409 _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 13 2019