A309317 a(n) is the maximum number of consecutive primes that can be produced as the differences of n integers.

1, 3, 4, 6, 10, 12, 15, 19, 22, 25, 30, 35, 38, 42, 48, 53, 59, 62, 68

Offset

2,2

Links

Table of n, a(n) for n=2..20.

Formula

n - 1 <= a(n-1) + 1 <= a(n) <= (n^2-n)/2 for any n >= 3. - Jinyuan Wang, Aug 03 2019

Example

For n = 2, (0, 2) gives 2 = 2 - 0.
For n = 3, (0, 2, 5) gives 2 = 2 - 0, 3 = 5 - 2, 5 = 5 - 0.
For n = 4, (0, 2, 3, 7) gives 2, 3, 5, 7.
For n = 5, (0, 2, 5, 6, 13) gives 2, 3, 5, 7, 11, 13.
For n = 6, (0, 6, 17, 19, 22, 29) gives 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
For n = 7, (0, 6, 7, 24, 26, 29, 37) gives 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
For n = 8, (0, 1, 5, 8, 29, 31, 42, 48) gives 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

Crossrefs

Sequence in context: A031132 A322165 A057477 * A249666 A113887 A103000

Adjacent sequences: A309314 A309315 A309316 * A309318 A309319 A309320

Keyword

nonn,more

Author

Andrey Borisov, Jul 23 2019

Status

approved