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Search: id:A080020
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| A080020 |
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Primes of the form q(n) = 370 + 18*binomial(ceiling(n/2),2) + 3*(-1)^n*(2*ceiling(n/2)-1). |
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+0
2
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| 367, 373, 379, 397, 409, 439, 457, 499, 523, 577, 607, 673, 709, 787, 829, 919, 967, 1069, 1123, 1237, 1297, 1423, 1489, 1627, 1699, 2089, 2347, 2437, 2719, 2917, 3019, 3229, 3559, 3673, 3907, 4027, 4273, 4657, 4789, 5059, 5197, 5479, 5623, 6067, 6373
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The smallest positive n for which q(n) is not prime is n=26.
Every q(n) is a divisor of some value of e(x) = x^2+x+41, the Euler prime-generating polynomial. Specifically, e(3*n^2-2*n+122) = q(2*n) * e(n-1) and e(3*n^2+2*n+122) = q(2*n+1) * e(n).
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EXAMPLE
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q(1)=367, q(25)=1699, q(98)=83*263, q(100)=22717, etc
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CROSSREFS
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Cf. A005846.
Sequence in context: A073305 A033174 A079493 this_sequence A118566 A142236 A054827
Adjacent sequences: A080017 A080018 A080019 this_sequence A080021 A080022 A080023
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KEYWORD
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nonn,easy
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AUTHOR
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Tewodros Amdeberhan (tewodros(AT)math.temple.edu), Jan 20 2003
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 20 2003
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