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A173079
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Positive integers n such that the sum S of 1 and first n^2-1 odd primes is divisible by n and S/n == n (mod 2).
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1
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2, 3, 12, 15, 17, 22, 35, 124, 191, 774, 1405, 1522, 3988, 6220, 7448, 8038, 11404, 63027, 161153
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OFFSET
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1,1
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COMMENTS
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A necessary condition for the existence of n X n magic square consisting of 1 and the first n^2-1 odd primes.
In 1913, J. N. Muncey proved that 12 is actually the smallest order for which such a magic square exists.
Squares of order 15, 17, 22, 35 and 124 were constructed by S. Tognon.
a(20) > 500000. - Donovan Johnson
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LINKS
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Table of n, a(n) for n=1..19.
Weisstein, Eric W. Prime Magic Square. MathWorld.
Stefano Tognon. Prime Magic Squares.
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CROSSREFS
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Cf. A064013, A073502, A073520, A164843.
Sequence in context: A015756 A163906 A180630 * A173903 A154785 A090512
Adjacent sequences: A173076 A173077 A173078 * A173080 A173081 A173082
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KEYWORD
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more,nonn
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AUTHOR
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Max Alekseyev, Feb 09 2010
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EXTENSIONS
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a(19) from Donovan Johnson, Nov 30 2010
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STATUS
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approved
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