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A075714
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1+n+n^s is a prime, s=18.
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2
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1, 2, 9, 24, 27, 44, 80, 251, 263, 311, 332, 356, 366, 371, 458, 515, 546, 548, 561, 566, 597, 599, 608, 650, 674, 713, 717, 722, 746, 762, 855, 867, 909, 969, 989, 993, 1010, 1011, 1022, 1052, 1064, 1191, 1245, 1269, 1275, 1284, 1355, 1376, 1431, 1473
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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=18 and find several first n's making n_s a prime (or a probable prime).
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EXAMPLE
| 2 is OK because at s=18, n=2, n_s=1+n+n^s=262147 is a prime.
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MATHEMATICA
| Select[Range[1800], PrimeQ[1+#+#^18]&] (* From Harvey P. Dale, Mar 24 2011 *)
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PROG
| (PARI) for(n=1, 1000, if(isprime(1+n+n^18), print1(n", ")))
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CROSSREFS
| Cf. A002384, A075713, A075715.
Sequence in context: A115185 A091107 A133469 * A101583 A204556 A185669
Adjacent sequences: A075711 A075712 A075713 * A075715 A075716 A075717
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Oct 03 2002
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EXTENSIONS
| More terms from R. Stephan (ralf(AT)ark.in-berlin.de), Apr 05 2003
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