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Minimal index of a Stanley antimagic square of order n consisting of distinct primes.
3

%I #28 Jan 09 2021 02:54:20

%S 2,16,53,150,395,774,1597,3036,5837,10080,18191

%N Minimal index of a Stanley antimagic square of order n consisting of distinct primes.

%C Stanley antimagic square of index d and order n is an n X n matrix where the sum of any n matrix elements in pairwise distinct rows and pairwise distinct columns equals d.

%H dxdy Forum, <a href="http://dxdy.ru/topic58862.html">Discussion at forum dxdy.ru</a> (in Russian)

%H Carlos Rivera, <a href="http://primepuzzles.net/puzzles/puzz_681.htm">Puzzle 681 Stanley Antimagic Squares</a>, The Prime Puzzles and Problems Connection.

%H Richard P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/ec1.pdf">Enumerative Combinatorics</a>, Vol. I, Exercises for Chapter 4, Exercise 53, p. 618.

%e For n=3 and d=53, we have the following square consisting of the primes:

%e 3 11 17

%e 5 13 19

%e 23 31 37

%e Here 3+13+37 = 3+19+31 = 11+19+23 = 11+5+37 = 17+13+23 = 17+5+31 = 53.

%K nonn,more

%O 1,1

%A _Natalia Makarova_, Jan 29 2013

%E Edited by _Max Alekseyev_, Feb 07 2013

%E Offset changed to 1 by _Jens Kruse Andersen_, Mar 30 2013

%E a(7) to a(10) from _Jens Kruse Andersen_, Mar 30 2013

%E a(11) from _Jens Kruse Andersen_, added by _Max Alekseyev_, May 05 2013

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Last modified September 23 09:28 EDT 2024. Contains 376154 sequences. (Running on oeis4.)