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A075716
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1+n+n^s is a prime, s=15.
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4
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1, 2, 30, 32, 35, 54, 62, 77, 101, 120, 138, 161, 171, 186, 210, 234, 269, 285, 311, 341, 362, 368, 374, 467, 476, 486, 531, 567, 578, 720, 737, 740, 780, 806, 824, 932, 990, 1035, 1037, 1041, 1049, 1067, 1089, 1136, 1137, 1146, 1167, 1202, 1251, 1269
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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 i consider the case s=15 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 OK because at s=15, n=2, n_s=1+n+n^s=32771 is a prime.
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MATHEMATICA
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Select[Range[1500], PrimeQ[1 + # + #^15] &] (* Harvey P. Dale, Dec. 13, 2010 *)
Select[Range[2000], PrimeQ[Total[#^Range[1, 15, 14]] + 1] &] (* Vincenzo Librandi, Jul 28 2014 *)
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PROG
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(PARI) for(n=1, 1000, if(isprime(1+n+n^15), print1(n", ")))
(Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^15]; // Vincenzo Librandi, Jul 28 2014
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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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