Search: id:A104238
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%I A104238
%S A104238 2,10,12,16,22,126,136,180,256,268,276,366,388,396,438,462,606,642,652,
%T A104238 658,676,738,760,768,982,1012
%N A104238 Positive integers n such that n^5 + 1 is semiprime.
%C A104238 n^5+1 can only be prime when n = 1, n^5+1 = 2. This is because of the 
               polynomial factorization n^5+1 = (n+1) * (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^4 - n^3 + n^2 - n + 1) are primes.
%F A104238 a(n)^5 + 1 is semiprime. a(n)+1 is prime and a(n)^4 - a(n)^3 + a(n)^2 
               - a(n) + 1 is prime.
%e A104238 n n^5+1 = (n+1) * (n^4 - n^3 + n^2 - n + 1)
%e A104238 2 33 = 3 * 11
%e A104238 10 100001 = 11 * 9091
%e A104238 12 248833 = 13 * 19141
%e A104238 16 1048577 = 17 * 61681
%Y A104238 Cf. A000040, A001538, A103854.
%Y A104238 Sequence in context: A053449 A060248 A092385 this_sequence A053069 A167503 
               A130842
%Y A104238 Adjacent sequences: A104235 A104236 A104237 this_sequence A104239 A104240 
               A104241
%K A104238 easy,nonn
%O A104238 1,1
%A A104238 Jonathan Vos Post (jvospost2(AT).com), Apr 02 2005

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