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A227956 Possible lengths of minimal prime number rulers. 0


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

%N Possible lengths of minimal prime number rulers.

%C 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.

%C 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.

%C a(n) is a finite subsequence of A008864.

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/PerfectRulers">Perfect and optimal rulers</a>.

%H Naoyuki Tamura, <a href="http://bach.istc.kobe-u.ac.jp/lect/ProLang/org/pnr.pdf">Complete List of Prime Number Rulers</a>, Information Science and Technology Center, Kobe University, 2013.

%e [0, 2, 3, 5, 7, 11, 17, 18] is a minimal and also a perfect prime number ruler.

%e [0, 2, 3, 5, 7, 11, 13, 19, 20] is a minimal but not a perfect prime number ruler.

%K nonn,fini,full

%O 1,1

%A _Peter Luschny_, Aug 26 2013

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.