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A075717
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1+n+n^13 is a prime.
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4
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1, 5, 15, 39, 50, 56, 105, 116, 128, 153, 168, 170, 243, 245, 264, 308, 314, 369, 401, 429, 480, 489, 531, 551, 599, 608, 680, 690, 699, 701, 785, 804, 939, 978, 1050, 1056, 1065, 1073, 1110, 1169, 1224, 1226, 1271, 1283, 1308, 1310, 1391, 1401
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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=13 and find several first n's making n_s a prime (or a probable prime).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1900
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EXAMPLE
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5 is OK because at s=13, n=2, n_s=1+n+n^s=1220703131 is a prime.
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MATHEMATICA
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Select[Range[1500], PrimeQ[1 + # + #^13] &] (* Harvey P. Dale, Apr 20 2013 *)
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PROG
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(PARI) n=0; for(k=1, 60, n=n+1; while(!isprime(1+n+n^13), n=n+1); print1(n", "))
(MAGMA) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^13]; // Vincenzo Librandi, Jul 28 2014
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CROSSREFS
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Cf. A002384, A075716, A075718.
Sequence in context: A142964 A188282 A014316 * A062487 A084447 A099035
Adjacent sequences: A075714 A075715 A075716 * A075718 A075719 A075720
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KEYWORD
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nonn,easy
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AUTHOR
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Zak Seidov, Oct 03 2002
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EXTENSIONS
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More terms from Ralf Stephan, Mar 20 2003
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STATUS
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approved
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