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A328815
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The smallest k such that one can form two sets of size n with distinct numbers from 1 to k with the property that the sum of any pair of numbers from different sets is a prime.
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0
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2, 4, 10, 31, 45, 85, 151, 253, 420, 775, 1303, 2521, 4641
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OFFSET
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1,1
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COMMENTS
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a(10) <= 775, because we can form these two sets:
{1, 61, 115, 151, 271, 295, 325, 361, 661, 775}
{12, 22, 162, 196, 348, 448, 462, 502, 658, 768}.
a(11) <= 1303, because we can form these two sets:
{4, 16, 58, 136, 178, 256, 268, 508, 586, 796, 1048}
{1, 13, 15, 133, 175, 253, 483, 505, 925, 1035, 1303}.
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LINKS
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EXAMPLE
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For n=3 one can use the sets {1, 3, 9} and {2, 4, 10}. The sum of every pair of numbers from different sets is prime: 1+2 = 3, 1+4 = 5, 1+10 = 11, 3+2 = 5, 3+4 = 7, 3+10 = 13, 9+2 = 11, 9+4 = 13, 9+10 = 19. The largest number in these sets is 10, hence a(3) = 10.
a(12) = 2521. One of the two solutions with all elements <= 2521 is the pair of sets
{1, 19, 49, 79, 175, 415, 595, 1405, 1531, 2311, 2359, 2521}
{88, 162, 192, 382, 568, 598, 708, 1012, 1152, 2062, 2202, 2292} (End).
a(13) = 4641. Unique solution is the pair of sets
{1, 21, 135, 561, 735, 1045, 1801, 1825, 2445, 3355, 3661, 3705, 4641}
{172, 262, 556, 592, 862, 886, 1018, 1732, 1978, 1996, 2656, 3592, 4462} (End).
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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