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Search: id:A114365
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| A114365 |
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Smallest prime in kx^3+x+1 is prime. |
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+0
1
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| 3, 19, 5, 7, 389, 59, 67, 11, 83, 13, 773, 107, 7177, 17, 131, 19, 2381, 163, 23, 179, 23011, 98321, 5407, 211, 29, 227, 31, 30011, 251, 2053, 57037, 7351, 37, 2309, 63949, 307, 41, 8647, 43, 2693, 347, 9511, 47, 23561, 379, 1327, 25609, 53, 419, 564367
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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There are no primes in the sequence for k = 4,18,48,...,n(n+1)^2. This is because n(n+1)^2x^3 + x + 1 = ((n+1)x+1)((n^2 + n)x^2 - nx + 1).
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PROGRAM
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(PARI) g2(n, p) = for(k=1, n, for(x=1, n, y=k*x^3+x+p; if(isprime(y), print1(y", "); break)))
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CROSSREFS
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Sequence in context: A101293 A078096 A139429 this_sequence A084559 A145688 A043073
Adjacent sequences: A114362 A114363 A114364 this_sequence A114366 A114367 A114368
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Feb 09 2006
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