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A309839
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a(n) = GAP_n: first integer m that is not the dimension of a semisimple subalgebra of M_n(k).
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2
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3, 6, 7, 12, 15, 22, 23, 42, 43, 48, 63, 76, 79, 96, 115, 140, 143, 166, 167, 192, 247, 248, 279, 312, 347, 384, 423, 472, 483, 526, 527, 572, 619, 624, 719, 724, 827, 832, 889, 948, 1009, 1072, 1087, 1152, 1219, 1288, 1359, 1432, 1507, 1520, 1597, 1676, 1679
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OFFSET
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2,1
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COMMENTS
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Define the sequence a(n) = GAP_n to be the smallest integer that is not the dimension of a semisimple subalgebra of M_n(k). This is one more than the upper endpoint of the continuous region of M_n(k). Because when n = 1 there are no gaps, this sequence begins at n = 2. See Heikoop paper, page 31.
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LINKS
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FORMULA
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a(n) > n^2 - 4 * sqrt(n + 2).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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