A329409 Lexicographically earliest sequence of distinct positive numbers such that among the pairwise sums of any seven consecutive terms there is exactly one prime sum.

1, 2, 7, 8, 13, 14, 19, 36, 20, 6, 26, 4, 16, 49, 28, 29, 23, 5, 9, 11, 17, 10, 15, 25, 35, 3, 39, 30, 24, 21, 27, 31, 18, 33, 12, 37, 45, 32, 40, 48, 38, 50, 42, 43, 22, 46, 34, 44, 52, 41, 53, 47, 58, 64, 57, 51, 59, 61, 60, 54, 63, 65, 56, 55, 69, 67, 66, 77, 68, 75, 78, 70, 72, 84, 62, 80, 81, 74, 71

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 have already the prime sum we need.
a(3) = 7 as a(3) = 3, 4, 5 or 6 would produce at least a prime sum too many.
a(4) = 8 as a(4) = 3, 4, 5 or 6 would again produce at least a 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) = 19 as a(7) = 15, 16, 17 or 18 would produce at least a prime sum too many.
a(8) = 36 is the smallest available integer that produces the single prime sum we need among the last 7 integers {2, 7, 8, 13, 14, 19, 36}, which is 43 = 36 + 7.
And so on.

Crossrefs

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

Sequence in context: A047239 A329410 A246389 * A231625 A032927 A004717

Adjacent sequences: A329406 A329407 A329408 * A329410 A329411 A329412

Keyword

nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 13 2019

Status

approved