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A027692
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a(n) = n^2 + n + 7.
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7
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7, 9, 13, 19, 27, 37, 49, 63, 79, 97, 117, 139, 163, 189, 217, 247, 279, 313, 349, 387, 427, 469, 513, 559, 607, 657, 709, 763, 819, 877, 937, 999, 1063, 1129, 1197, 1267, 1339, 1413, 1489, 1567, 1647, 1729, 1813, 1899, 1987, 2077, 2169, 2263
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OFFSET
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0,1
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COMMENTS
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Integers k for which the discriminant of x^3-k*x-k is a square. - Jacob A. Siehler, Mar 14 2009
Integers k for which the Galois group of the polynomial x^3 - k*x - k over Q is a cyclic group of order 3. See Conrad, Corollary 2.5. - Peter Bala, Oct 17 2021
Integers k such that 4*k - 27 is a square.
Integers k for which the Galois group of the polynomial x^3 + k*(x + 1)^2 over Q is the cyclic group C_3 (apply Conrad, Corollary 2.5 and Uchida, Lemma 1).
For the primes in this list see A005471. (End)
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LINKS
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FORMULA
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G.f.: (-7 + 12*x - 7*x^2) / (x-1)^3. - R. J. Mathar, Feb 06 2011
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*3*sqrt(3)/2)/(3*sqrt(3)). - Amiram Eldar, Jan 17 2021
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MAPLE
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n*(n+1)+7 ;
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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