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

1,2

Links

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

Example

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.

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.

Sequence in context: A129850 A037073 A358535 * A329408 A047239 A329410

Adjacent sequences: A329404 A329405 A329406 * A329408 A329409 A329410

Keyword

nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

Status

approved