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A060566
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a(n) = n^2 - 79*n + 1601.
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8
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1601, 1523, 1447, 1373, 1301, 1231, 1163, 1097, 1033, 971, 911, 853, 797, 743, 691, 641, 593, 547, 503, 461, 421, 383, 347, 313, 281, 251, 223, 197, 173, 151, 131, 113, 97, 83, 71, 61, 53, 47, 43, 41, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601, 1681
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OFFSET
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0,1
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COMMENTS
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a(n) is prime for 0 <= n <= 79. a(80) = 1681 = 41^2.
More than the usual number of terms are shown in order to display the initial 80 primes.
First 80 prime entries are palindromically distributed because a(n) = P(x) = x^2 + x + 41, with x=n-40 and we observe that P(x) generates primes (A005846) for x = 0 through 39, along with the fact that P(-x) = P(x-1). - Lekraj Beedassy, Apr 24 2006
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 6.
C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Dover Publications, NY, 1966, p. 37, 147.
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LINKS
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FORMULA
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G.f.: (1601 - 3280*x + 1681*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
(End)
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MAPLE
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MATHEMATICA
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Table[n^2-79*n+1601, {n, 100}] (* or *) LinearRecurrence[{3, -3, 1}, {1523, 1447, 1373}, 100] (* Harvey P. Dale, Jan 14 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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