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A099481
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Numbers k such that 2^k - k^2 is a semiprime.
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2
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11, 13, 15, 21, 23, 37, 39, 41, 43, 47, 49, 55, 67, 75, 103, 105, 133, 147, 153, 161, 163, 177, 201, 209, 221, 239, 249, 263, 311, 335, 355, 397, 413, 421, 437, 447, 583, 617, 775, 807
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OFFSET
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1,1
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COMMENTS
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The smaller prime factor of the 125-digit semiprime 2^413 - 413^2 has 40 digits; for the 127-digit semiprime 2^421 - 421^2 the smaller prime factor has 45 digits. The next term is >= 583. - Hugo Pfoertner, Oct 14 2007
The factorization of the 176-decimal-digit composite 2^583 - 583^2 using SNFS in YAFU took 55000 seconds on 4 cores of an i5-2400 CPU @ 3.10GHz. a(38) >= 617. - Hugo Pfoertner, Jul 23 2019
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LINKS
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EXAMPLE
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a(1) = 11 because 2^11 - 11^2 = 1927 = 41*47.
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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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