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