A329407 Among the pairwise sums of any five consecutive terms there is exactly one prime sum; lexicographically earliest such sequence of distinct positive numbers.

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, 22, 33, 24, 27, 28, 36, 29, 34, 35, 40, 31, 41, 37, 44, 38, 43, 39, 42, 45, 46, 47, 48, 49, 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

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

Keywords

• nonn

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 at least one prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least one prime sum too many.
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.
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.
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).

Cf. A329405: no prime among the pairwise sums of 3 consecutive terms.

Cf. A329406 .. A329410: exactly 1 prime sum using 4, ..., 10 consecutive terms.

Cf. A329411 .. A329416: exactly 2 prime sums using 3, ..., 10 consecutive terms.

See also A329450, A329452 onwards for "nonnegative" variants.