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.

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, 23, 28, 30, 32, 33, 31, 29, 34, 36, 35, 40, 41, 39, 37, 38, 42, 43, 45, 44, 47, 46, 50, 48, 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

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

Keywords

• nonn

Comments

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

Examples

			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 our prime sum.
a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce one prime sum too many.
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.
And so on.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A329333 (3 consecutive terms, exactly 1 prime sum). See also A329450, A329452 onwards.