cp's OEIS Frontend

A329406 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any four consecutive terms there is exactly one prime sum.

%I A329406 #27 Nov 28 2019 11:01:06
%S A329406 1,2,7,8,4,14,11,5,10,3,15,6,13,9,12,16,17,18,19,21,27,24,22,20,25,26,
%T A329406 23,28,30,32,33,31,29,34,36,35,40,41,39,37,38,42,43,45,44,47,46,50,48,
%U A329406 49,56,62,52,53,54,58,57,51,59,68,55,60,63,64,61,65,67,74,69,72,70,66,71,75,77,76,78
%N A329406 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any four consecutive terms there is exactly one prime sum.
%C A329406 For all n >= 1, there is exactly one prime in {a(n+i) + a(n+j), 0 <= i < j <= 3}. See A329450, A329452 onwards for variants for nonnegative integers. - _M. F. Hasler_, Nov 14 2019
%H A329406 Jean-Marc Falcoz, <a href="/A329406/b329406.txt">Table of n, a(n) for n = 1..10000</a>
%e A329406 a(1) = 1 by minimality.
%e A329406 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 A329406 a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce one prime sum too many.
%e A329406 a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce one prime sum too many.
%e A329406 a(5) = 4 as a(5) = 3 would produce two primes instead of one (3 + 2 = 5 and 3 + 8 = 11); with a(5) = 4 we have the single prime sum we need among the last 4 integers {2,7,8,4}: 11 = 4 + 7.
%e A329406 And so on.
%Y A329406 Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.
%K A329406 nonn
%O A329406 1,2
%A A329406 _Eric Angelini_ and _Jean-Marc Falcoz_, Nov 13 2019