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%I #13 Jul 30 2015 23:16:08
%S 2,6,12,232,262,280,330,430,508,772,786,852,1012,1522,1566,1626,1810,
%T 2346,2556,2676,3658,3888,3910,4018,4048,4258,4830,5188,5322,5478,
%U 5848,6090,6366,6568,7018,7458,7602,7606,7822,8178,8928,9420,9618,9676,10398
%N Positive integers n such that n^11 + 1 is semiprime.
%C We have the polynomial factorization n^11+1 = (n+1) * (n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1). Hence after the initial n=1 prime the binomial can at best be semiprime and that only when both (n+1) and (n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1) are primes.
%H Robert Price, <a href="/A105122/b105122.txt">Table of n, a(n) for n = 1..4303</a>
%F a(n)^11+1 is semiprime A001538. a(n)+1 is prime and a(n)^10 - a(n)^9 + a(n)^8 - a(n)^7 + a(n)^6 - a(n)^5 + a(n)^4 - a(n)^3 + a(n)^2 - a(n) + 1 is prime.
%e 2^11+1 = 2049 = 3 * 683,
%e 6^11+1 = 362797057 = 7 * 51828151,
%e 1012^11+1 = 1140212079231804336089593374834689 = 1013 * 1125579545144920371263172137053.
%t Select[ Range[10721], PrimeQ[ # + 1] && PrimeQ[(#^11 + 1)/(# + 1)] &] (* _Robert G. Wilson v_, Apr 09 2005 *)
%Y Cf. A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 08 2005
%E More terms from _Robert G. Wilson v_, Apr 09 2005
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