A329408 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any six consecutive terms there is exactly one prime sum.

1, 2, 7, 8, 13, 14, 12, 20, 4, 22, 35, 10, 6, 16, 28, 29, 5, 34, 21, 15, 3, 11, 17, 18, 9, 27, 31, 19, 33, 24, 25, 32, 30, 26, 36, 38, 39, 40, 42, 46, 48, 45, 23, 54, 69, 37, 43, 41, 50, 44, 47, 49, 55, 61, 53, 62, 51, 57, 59, 63, 60, 58, 52, 64, 56, 77, 67, 65, 68, 66, 75, 78, 70, 74, 72, 80, 73, 71, 81

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 the prime sum we need.
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) = 14 as a(6) = 14 doesn't produce an extra prime sum - only composite sums.
a(7) = 12 as 12 is the smallest available integer that produces the single prime sum we need among the last 6 integers {2,7,8,13,14,12}, which is 19 = 12 + 7.
And so on.

Crossrefs

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

Sequence in context: A037073 A358535 A329407 * A047239 A329410 A246389

Adjacent sequences: A329405 A329406 A329407 * A329409 A329410 A329411

Keyword

nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

Status

approved