A227956 Possible lengths of minimal prime number rulers.

3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 44, 62

Offset: 1

Author

Peter Luschny, Aug 26 2013

Keywords

• nonn
• fini
• full

Comments

A ruler is a prime number ruler provided all its interior marks are on a prime number position. A ruler is called complete when any positive integer distance up to the length of the ruler can be measured. A complete ruler is called minimal when any subsequence of its marks is not complete for the same length. A complete ruler is perfect, if there is no complete ruler with the same length which possesses fewer marks. A perfect ruler is minimal (but not conversely). For definitions, references and links related to complete rulers see A103294.

The possible lengths of perfect prime number rulers are: 3, 4, 6, 8, 14, 18, 20, 24, 30, 32. There are 102 prime number rulers in total, 28 of which are minimal prime number rulers and 12 perfect prime number rulers.

a(n) is a finite subsequence of A008864.

Examples

			[0, 2, 3, 5, 7, 11, 17, 18] is a minimal and also a perfect prime number ruler.
[0, 2, 3, 5, 7, 11, 13, 19, 20] is a minimal but not a perfect prime number ruler.
		

Links

• Peter Luschny, Perfect and optimal rulers.
• Naoyuki Tamura, Complete List of Prime Number Rulers, Information Science and Technology Center, Kobe University, 2013.