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| A307246
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Smallest k for which a set of n primes <= k exists so that the averages of all nonempty subsets are all distinct primes.
(history;
published version)
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#11 by Peter Luschny at Mon Apr 01 08:34:39 EDT 2019
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#10 by Joerg Arndt at Mon Apr 01 01:52:39 EDT 2019
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#9 by Jon E. Schoenfield at Sun Mar 31 23:19:53 EDT 2019
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#8 by Jon E. Schoenfield at Sun Mar 31 23:19:40 EDT 2019
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| NAME
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Smallest k for which a set of n primes <= k exists so that the averages of all non-emptynonempty subsets are all distinct primes.
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| EXAMPLE
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For any set of n elements, there are 2^n - 1 non-emptynonempty subsets.
The averages of the 2^3 - 1 = 7 non-emptynonempty subsets are:
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| CROSSREFS
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For n> > 1, largest element of row n of A113833.
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| STATUS
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reviewed
editing
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Discussion
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| Sun Mar 31
| 23:19
| Jon E. Schoenfield: ("nonempty", per the OEIS Style Sheet)
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#7 by Joerg Arndt at Sun Mar 31 02:14:21 EDT 2019
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#6 by Bert Dobbelaere at Sat Mar 30 13:16:04 EDT 2019
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#5 by Bert Dobbelaere at Sat Mar 30 13:01:23 EDT 2019
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| LINKS
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Andrew Granville, , <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">Prime number patterns</a>
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Discussion
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| Sat Mar 30
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| Bert Dobbelaere: Sequence existed in table form only.
Performed independent confirmation of the results of A. Granville and T. D. Noe.
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#4 by Bert Dobbelaere at Sat Mar 30 13:00:14 EDT 2019
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| LINKS
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Andrew Granville, Prime number patterns
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#3 by Bert Dobbelaere at Sat Mar 30 12:48:34 EDT 2019
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| NAME
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allocatedSmallest k for which a set of n primes <= k exists so that the averages of all non-empty subsets are all Bertdistinct Dobbelaereprimes.
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| DATA
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2, 7, 67, 1277, 2484733
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| OFFSET
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1,1
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| EXAMPLE
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For any set of n elements, there are 2^n - 1 non-empty subsets.
For n=3, consider the set {7, 19, 67}.
The averages of the 2^3 - 1 = 7 non-empty subsets are:
avg({7}) = 7
avg({19}) = 19
avg({67}) = 67
avg({7, 19}) = 13
avg({7, 67}) = 37
avg({19, 67}) = 43
avg({7, 19, 67}) = 31
All these averages are different primes, and no such set exists with the largest element < 67. Hence, a(3) = 67.
Sets which minimize the largest elements are:
n = 1 {2}
n = 2 {3, 7}
n = 3 {7, 19, 67}
n = 4 {5, 17, 89, 1277}
n = 5 {209173, 322573, 536773, 1217893, 2484733}
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| CROSSREFS
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For n>1, largest element of row n of A113833.
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| KEYWORD
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allocated
nonn,hard,more
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| AUTHOR
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Bert Dobbelaere, Mar 30 2019
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| STATUS
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approved
editing
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#2 by Bert Dobbelaere at Sat Mar 30 12:48:34 EDT 2019
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| NAME
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allocated for Bert Dobbelaere
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| KEYWORD
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recycled
allocated
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