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A075715
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Numbers n such that n^16 + n + 1 is prime.
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4
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1, 2, 21, 26, 47, 65, 99, 102, 206, 215, 216, 257, 294, 342, 437, 441, 537, 540, 702, 747, 837, 860, 909, 912, 921, 926, 942, 1020, 1071, 1101, 1112, 1125, 1181, 1254, 1266, 1322, 1344, 1364, 1370, 1406, 1422, 1665, 1814, 1821, 1829, 1905, 2024
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OFFSET
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1,2
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COMMENTS
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For s = 5, 8, 11, 14, 17, 20, ..., n_s = 1 + n + n^s is always composite for any n > 1. Also at n = 1, n_s = 3 is a prime for any s. So it is interesting to consider only the cases of s =/= 5, 8, 11, 14, 17, 20, ... and n > 1. Here we consider the case s = 16 and find several first n's making n_s a prime (or a probable prime).
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LINKS
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EXAMPLE
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2 is in the sequence because 1 + 2 + 2^16 = 65539 is prime.
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MAPLE
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MATHEMATICA
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PROG
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(PARI) for(n=1, 3000, if(isprime(1+n+n^16), print1(n", ")))
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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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EXTENSIONS
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STATUS
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approved
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